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The purpose of this paper is to propose the new dependences of cycles to failure for a given initial crack length upon the stress amplitude in the linear fracture approach. The anticipated unified propagation function describes the infinitesimal crack-length growths per increasing number of load cycles, supposing that the load ratio remains constant over the load history. Two unification functions with different number of fitting parameters are proposed. On one hand, the closed-form analytical solutions facilitate the universal fitting of the constants of the fatigue law over all stages of fatigue. On the other hand, the closed-form solution eases the application of the fatigue law, because the solution of nonlinear differential equation turns out to be dispensable. The main advantage of the proposed functions is the possibility of having closed-form analytical solutions for the unified crack growth law. Moreover, the mean stress dependence is the immediate consequence of the proposed law. The corresponding formulas for crack length over the number of cycles are derived.

In this paper, the method of representation of crack propagation functions through appropriate elementary functions is employed. The choice of the elementary functions is motivated by the phenomenological data and covers a broad region of possible parameters. With the introduced crack propagation functions, differential equations describing the crack propagation are solved rigorously.

The resulting closed-form solutions allow the evaluation of crack propagation histories on one hand, and the effects of stress ratio on crack propagation on the other hand. The explicit formulas for crack length over the number of cycles are derived.

In this paper, linear fracture mechanics approach is assumed.

Shortening of evaluation time for fatigue crack growth. Simplification of the computer codes due to the elimination of solution of differential equation. Standardization of experiments for crack growth.

This paper introduces the closed-form analytical expression for crack length over number of cycles. The new function that expresses the damage growth per cycle is also introduced. This function allows closed-form analytical solution for crack length. The solution expresses the number of cycles to failure as the function of the initial size of the crack and eliminates the solution of the nonlinear ordinary differential equation of the first order. The different common expressions, which account for the influence of the stress ratio, are immediately applicable.

In this work, the cohesive zone model (CZM) developed by some of the authors to simulate the propagation of fatigue defects in two dimensions is extended in order to simulate the propagation of defects in 3D. The paper aims to discuss this issue.

The procedure has been implemented in the finite element (FE) solver (Abaqus) by programming the appropriate software-embedded subroutines. Part of the procedure is devoted to the calculation of the rate of energy release per unit, G, necessary to know the growth of the defect.

The model was tested on different joint geometries, with different load conditions (pure mode I, mode II pure, mixed mode I/II) and the results of the analysis were compared with analytical solutions or virtual crack closure technique (VCCT).

The possibility to simulate the growth of a crack without any re-meshing requirements and the relatively easy possibility to manipulate the constitutive law of the cohesive elements makes the CZM attractive also for the fatigue crack growth simulation. However, differently from VCCT, three-dimensional fatigue de-bonding/delamination with CZM is not yet state-of-art in FE softwares.

Recently, a new class of fatigue crack growth models based on elastoplastic stress‐strain histories at the crack tip region and strain‐life fatigue damage models have been proposed. The fatigue crack propagation is understood as a process of continuous crack initializations, over elementary material blocks, which may be governed by strain‐life data of the plain material. The residual stresses developed at the crack tip play a central role in these models, since they are used to assess the actual crack driving force, taking into account mean stresses and loading sequential effects. The UniGrow model fits this particular class of fatigue crack propagation models. The purpose of this paper is to propose an extension of the UniGrow model to derive probabilistic fatigue crack propagation data, in particular the derivation of the P–da/dN–ΔK–R fields.

An existing deterministic fatigue crack propagation model, based on local strain‐life data is first assessed. In particular, an alternative methodology for residual stress computation is proposed, based on elastoplastic finite element analysis, in order to overcome inconsistencies found in the analytical approximate approaches often used in literature. Then, using probabilistic strain‐life fields, a probabilistic output for the fatigue crack propagation growth rates is generated. A new probabilistic fatigue field is also proposed to take mean stress effects into account, using the Smith‐Watson‐Topper (SWT) damage parameter. The proposed models are assessed using experimental data available for two materials representative from old Portuguese bridges.

A new method to generate probabilistic fatigue crack propagation rates (P–da/dN–ΔK–R fields) is proposed and verified using puddle iron from old Portuguese bridges, usually characterized by significant scatter in fatigue properties. Also, a new probabilistic fatigue field for plain material is proposed to deal with mean stress effects.

A relation between the P–ε–N and the P–da/dN–ΔK–R fields is firstly proposed in this research. Furthermore, a new P–SWT–N field is proposed to deal with mean stress effects.

Within the context of an international conference dealing with global challenges, the Atlantic Community and the outlook for international order organized by Webster University, Geneva (Switzerland), to propose an approach to strengthening the international order by reviving the global responsibility to abide by fundamental humanitarian rules.

The twentieth century presented a very disturbing catalog of violations of humanitarian law. In addressing the main question of the conference, namely “What are the true principles of international order today and do we need new rules and organizing principles in the future?”, the author tackles the issue from the international humanitarian law perspective and suggests various instruments (formal and informal) for enhancing the protection of human dignity.

A global responsibility to abide by fundamental humanitarian rules may be revived through positive law and judicial mechanisms, but also through a new respect for human life, a return to universal values found in all civilizations, religions and traditions, and through a new humanitarian order based on the core concept of humanity.

This paper suggests that it is through a combination of existing legal and humanitarian instruments, and not just one, that the international order can be strengthened.

The purpose of this paper is to develop an approach to optimize the cycles‐to‐failure of a peened component with respect to laser peening (LP) variables: pressure magnitude, mid‐span, and spot size when the component is subject to a variable amplitude loading.

To optimally design an LP process, an experimentally validated 3D finite element simulation of the LP process, a cycles‐to‐failure estimation capability incorporating residual stress, and a particle swarm optimization strategy were developed and employed to maximize the cycles‐to‐failure of a component of a titanium turbine disk.

The most critical finding of this research is that a minor difference in the residual stress profile can lead to a large difference in the cycles‐to‐failure. This finding implies that selecting the optimization objective to be the cycles‐to‐failure is a better option as compared to the residual stress profile.

The LP‐induced residual stresses are assumed static and do not change as number of load cycles increase.

The paper develops a framework that relates the LP variables and the cycles‐to‐failure of a peened component. A modified particle swarm optimization approach is developed to optimize the fatigue life of a turbine disk.

To develop a new computational tool for predicting failure probability of structural/mechanical systems subject to random loads, material properties, and geometry.

High dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for capturing the high‐dimensional relationships between sets of input and output model variables. It is a very efficient formulation of the system response, if higher order variable correlations are weak and if the response function is dominantly of additive nature, allowing the physical model to be captured by the first few lower order terms. But, if multiplicative nature of the response function is dominant then all right hand side components of HDMR must be used to be able to obtain the best result. However, if HDMR requires all components, which means 2^N number of components, to get a desired accuracy, making the method very expensive in practice, then factorized HDMR (FHDMR) can be used. The component functions of FHDMR are determined by using the component functions of HDMR. This paper presents the formulation of FHDMR approximation of a multivariate limit state/performance function, which is dominantly of multiplicative nature. Given that conventional methods for reliability analysis are very computationally demanding, when applied in conjunction with complex finite element models. This study aims to assess how accurately and efficiently HDMR/FHDMR based approximation techniques can capture complex model output uncertainty. As a part of this effort, the efficacy of HDMR, which is recently applied to reliability analysis, is also demonstrated. Response surface is constructed using moving least squares interpolation formula by including constant, first‐order and second‐order terms of HDMR and FHDMR. Once the response surface form is defined, the failure probability can be obtained by statistical simulation.

Results of five numerical examples involving structural/solid‐mechanics/geo‐technical engineering problems indicate that the failure probability obtained using FHDMR approximation for the limit state/performance function of dominantly multiplicative in nature, provides significant accuracy when compared with the conventional Monte Carlo method, while requiring fewer original model simulations.

This is the first time where application of FHDMR concepts is explored in the field of reliability and system safety. Present computational approach is valuable to the practical modeling and design community, where user often suffers from the curse of dimensionality.

The purpose of this paper is to determine the ultra-high cycle fatigue behavior and ultra-slow crack propagation behavior of selective laser melting (SLM) AlSi7Mg alloy under as-built conditions.

Constant amplitude and two-step variable amplitude fatigue tests were carried out using ultrasonic fatigue equipment. The fracture surface of the failure specimen was quantitatively analyzed by scanning electron microscope (SEM).

The results show that the competition of surface and interior crack initiation modes leads to a duplex S–N curve. Both manufacturing defects (such as the lack of fusion) and inclusions can act as initially fatal fatigue microcracks, and the fatigue sensitivity level decreases with the location, size and type of the maximum defects.

The research results play a certain role in understanding the ultra-high cycle fatigue behavior of additive manufacturing aluminum alloys. It can provide reference for improving the process parameters of SLM technology.

I. The Gendarmerie: Historical Background The Gendarmerie is the senior unit of the French Armed Forces. It is, however, difficult to give a precise date to its creation. What can be asserted is that as early as the Eleventh Century special units existed under the sénéchal (seneschal), an official of the King's household who was entrusted with the administration of military justice and the command of the army. The seneschal's assistants were armed men known as sergents d'armes (sergeants at arms). In time, the office of the seneschal was replaced by that of the connétable (constable) who was originally the head groom of the King's stables, but who became the principal officer of the early French kings before rising to become commander‐in‐chief of the army in 1218. The connétable's second in command was the maréchal (marshal). Eventually, the number of marshals grew and they were empowered to administer justice among the soldiery and the camp followers in wartime, a task which fully absorbed them throughout the Hundred Years War (1337–1453). The corps of marshals was then known as the maréchaussée (marshalcy) and its members as sergeants and provosts. One of the provosts, Le Gallois de Fougières, was killed at Agincourt in 1415; his ashes were transferred to the national memorial to the Gendarmerie, which was erected at Versailles in 1946.

The purpose of this paper is to examine the ongoing “new extraction” on the African continent. Contrary to mainstream scholarship and policies that see in law an external variable to remedy the “resource curse,” this paper channels attention toward the role of law as an institution of extraction in the longue durée. Unpacking the close association of law with the conversion of economic surpluses and power into enduring social relationships can help trace the mechanisms by which the uneven and unequal connection between Africa and the world is being negotiated, justified and challenged over time.

To this end, this paper deploys an approach anchored in political sociology of law and focuses on the roles played specifically by lawyers to trace the “interconnectedness” between European colonialism on the continent and the consolidation of the contemporary international economic and legal political order. It illustrates this approach with the case study of the “Africa” Bar in Paris as a key site in which extractive deals between multinational corporations and Francophone African states are negotiated.

This micro focus helps to explain the dual position of the “Africa” Bar in Paris, as offshore yet connected as it is shaped by both imperial legacies and ongoing waves of globalization into the African continent.

This approach traces a more nuanced explanation of Africa’s unequal and uneven relationship with the global economy as one shaped by the path of imperial legacies and successive and interconnected waves of globalization across Africa.

The trajectory of François Perroux across the Vichy regime poses about all possible range of methodological issues to the historian of ideas: individual versus collective biography, ideational versus ideological reading, internal versus external analysis, etc. The chapter outlines key elements about Perroux’s trajectory showing the entanglements and boundaries of science and politics in the transition from democratic to authoritarian rule and vice versa. A particular emphasis on uncertainties and adjustments shows, against the tendency to a teleological explanation induced by a linear interpretation of his career, that different paths were considered by Perroux, but that his choices were nevertheless constrained by the forces of both the scientific and political fields.