Von Mises yield criterion

Résumé

In continuum mechanics, the maximum distortion criterion (also von Mises yield criterion) states that yielding of a ductile material begins when the second invariant of deviatoric stress J_2 reaches a critical value. It is a part of plasticity theory that mostly applies to ductile materials, such as some metals. Prior to yield, material response can be assumed to be of a nonlinear elastic, viscoelastic, or linear elastic behavior. In materials science and engineering, the von Mises yield criterion is also formulated in terms of the von Mises stress or equivalent tensile stress, \sigma_\text{v}. This is a scalar value of stress that can be computed from the Cauchy stress tensor. In this case, a material is said to start yielding when the von Mises stress reaches a value known as yield strength, \sigma_\text{y}. The von Mises stress is used to predict yielding of materials under complex loading from the results of uniaxial tensile tests. The von

Source officielle

https://en.wikipedia.org/wiki/Von_Mises_yield_criterion

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A Simple Criterion for Non-relative Hyperbolicity and One-endedness of Groups

2005

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The objective of this thesis is to improve methods for predicting the fatigue life, multiaxial or not, of mild- and more particularly high-strength steels using local approaches that have the capacity to be applicable to almost any cases, hence the term generalized local approaches. More specifically, the most suited and practical generalized stress-based approaches are determined and the framework for a 3D generalized approach based on an existing novel continuum strain-based one for 2D is developed. To achieve this objective, at first, several multiaxial fatigue tests are carried out on two representative welded details. These welded specimens are made of S690QL HSS and some of conventional S235JR structural mild steel. Advanced measurements techniques are used to quantify the parameters that drive the fatigue life and to determine the various stages of the fatigue damage process. Then, various multiaxial fatigue stress-based criteria are used in combination to the effective notch stress local approach to estimate multiaxial fatigue life of the tested specimens and of a database obtained from the literature. The results are statistically analyzed to help determine the most reliable multiaxial fatigue stress-based criteria and the ones that should be avoided, as well as their relative FAT categories based on various statistical approaches proposed in the EC3, IIW and in the literature. The von Mises equivalent stress expressed from stress ranges and the more complex and advanced Findley and Carpinteri-Spagnoli criteria have proven to be very well suited to study uniaxial and multiaxial fatigue under constant amplitude proportional and non-proportional loading, leading to safe estimation if combined to the proposed or updated FAT categories. On the contrary, the principal stress criterion has been shown to be inaccurate and leads to unsafe estimations as soon as multiaxial loading are involved. Thirdly, the novel continuum strain-based approach generalization in 3D is presented. This approach allows to precisely estimate each step of the fatigue damage process, including initiation, short crack propagation and propagation up to the final fracture, taking into account even more parameters than the previous local stress-based approaches. To estimate the fatigue effective stress in the damage process zone, the proposed generalized local approach is based on a so-called "area method". The equivalent fatigue effective strain time history is deduced from the fatigue effective stress time history using a continuum single element model (CSEM), validated under different individual loadings. The proposed approach allows to account accurately for complex elastic-plastic material behavior while avoiding effects of finite element singularities, mainly at the crack tip. The effect of mean stress is modelled while the effect of the residual stresses is also considered but in a simplified manner. Finally, the influence of the most important parameters that govern fatigue life, mentioned previously, is assessed by mean of parametrical analysis using the continuum strain-based approach. Estimated initiation fatigue lives and crack plane angles are shown to compare well with experimental data, determined by help of stereo Digital Image Correlation (DIC) measurements.

EPFL2020

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Builders have always been concerned about the durability of construction materials and building components. Nowadays, powerful information technology tools offer an opportunity to approach the complexity of aging phenomena in an innovative way. This thesis presents a method and a simulation model designed to predict the aging of multi-layer building components. Integrated into a software tool, they take into account the nature and intensity of the external agents acting on a component. The tool creates possibilities for a variety of applications : it can guide users towards the most appropriate and durable construction systems, it can be helpful in decision making for building maintenance and it can provide service-life information for life-cycle analysis (LCA). The work is based on research undertaken between 1990 and 1997 by the Expert Service from the Construction and Conservation Laboratory (LCC) at the Ecole Polytechnique Fédérale de Lausanne (EPFL) in collaboration with the ARIA-laboratory of the Ecole Nationale Supérieure d'Architecture de Lyon (UMR CNRS n°694 MAP, Hervé Lequay) for the development of the Assistance to Maintenance of Buildings tool (AMB). The goal of the present work was to continue and extend the previous investigations. In a first step, the tool has been analysed and recreated within the Delphi development environment. New parameter recorder modules and graphical analysing modules have been added for better simulation monitoring and visualisation of chain reactions due to degradation processes. The model has also been adapted to allow stochastic simulation with the Monte-Carlo Method. This part of the research permits bringing out the structure of the simulation method's various aspects and concepts and working out its detailed description. In the report, global aspects of the prediction method are presented first. Basic concepts and principles, such as stress actions, material performance and element functions, are described. In a second part, the design of the computer model is presented. The aim is to show how the general concepts of the method can find an application. Various stress agents and specific material performances that participate in the aging process and lead to a decrease in performance are highlighted. Aging is simulated by the interaction between the materials and agents over time. Definitions of the failure criteria for a given building component are made by identification of its functions and assigning performance limits values. Two chapters are dedicated to the detailed description of the different stress agents and performances used in the model. These are followed by a selection of case studies that shows the working of the simulation and illustrates the various types of results that can be obtained. The conclusions reiterate that the prediction of construction material aging is a wide and complex subject. To be able to make not only qualitative but also quantitative durability predictions, further research must be undertaken in different domains. This is necessary in order to collect existing knowledge and to obtain missing information. As the presented method and model can easily integrate new data as it becomes available, they could play the role of a development platform for future investigations. This would allow a progressive increase in the reliability of the predictions.

EPFL2010

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EPFL2010

EPFL2020