A probabilistic high cycle fatigue model applied to cast Al-Si alloys

In this work, the high cycle fatigue behavior of cast hypo-eutectic Al-Si alloys is investigated. It is observed that two different coexisting fatigue initiation mechanisms can occur in these materials depending on the presence of different microstructural heterogeneities (i.e. micro-shrinkage pores, Si particles, Fe-rich inter-metallics, DAS of the Al-matrix, etc).Firstly, an experimental study is presented, highlighting the coexistence of these two fatigue damage mechanisms and their dependence on the presence of different micro-structural heterogeneities. A probabilistic high cycle fatigue model, which has the capacity to describe these two mechanisms, is then presented. The model contains the same principal ingredients as the one developed by [1]. It uses a probabilistic framework to link the two different fatigue damage mechanisms, and can take into account the mean stress and the effect of a biaxial stress state.This work was undertaken in partnership with PSA Peugeot Citrooën and was financially supported by the French region, Pays de la Loire

A Biaxial Fatigue Specimen for Uniaxial Loading

The aim of this paper is to present a novel un-notched fatigue test specimen in which a biaxial stress state is achieved using a uniaxial loading condition. This allows the problem of multi-axial fatigue to be studied using relatively common one-axis servo-hydraulic testing machines. In addition the specimen presented here is very compact and can be made using a small volume of material (100x40x4.5mm). For this specimen, the degree of biaxiality, defined by the parameter is equal to approximately 0.45. The specimen geometry was optimised using the Dang Van multi-axial fatigue criterion. In addition to use as a fatigue specimen, it has been demonstrated that the biaxial specimen presented here is also suitable for biaxial tensile tests, to determine the rupture strength of a material in a biaxial stress state. Two different materials have been investigated: The first was wrought aluminium 2024-O in the form of 5mm sheets. The second was a cast aluminium-silicon alloy AlSi7Cu0.5Mg0.3, commonly used in automotive and aeronautical applications. The fatigue strengths were determined at 2x106 cycles and at various R-ratios using a staircase procedure. For the aluminium 2024, it is shown that the biaxial stress state increases the maximum permissible first principal stress when compared to the uniaxial condition. However, in terms of the cast aluminium alloy, it has been demonstrated that this type of fatigue specimen is not suitable for materials containing casting defects, in particular micro-shrinkage pores, because the volume of material, in which the stress state is biaxial, is not large enough.The authors gratefully acknowledge the financial support of PSA – Peugeot Citroën and also that of the Conseil Général du Département de Maine-et-Loire, France

A flexible HCF modeling framework leading to a probabilistic multiaxial Kitagawa-Takahashi diagram

This article describes a flexible modeling framework which leads to the construction of a probabilistic, multiaxial Kitagawa-Takahashi diagram. This framework has been developed following experimental observations that clearly indicate that two independent fatigue damage mechanisms can be activated, at the same time, in metallic materials. Specifically, one damage mechanism is associated with crack initiation and the other with crack arrest. It is postulated that these damage mechanisms are more appropriately modeled using two different fatigue criteria or, more specifically, two completely different approaches to fatigue (i.e. a classical multiaxial fatigue criterion and a LEFM type criterion). Hence, the proposed modeling framework provides the possibility of combining any two suitable criteria, in a probabilistic framework based on the weakest link hypothesis and results in the continuous description of the Kitagawa diagram for any multiaxial stress state. It is shown that under certain conditions this approach is equivalent to the classical El Haddad approach to the short crack problem encountered in LEFM. However, the proposed framework is easily extended to multiaxial loading conditions. This modeling framework is demonstrated in detail via its application to multiaxial fatigue data for data taken from the literature

Machine d'essai en fatigue biaxiale disposant d'une éprouvette

Machine d'essai en fatigue disposant d'une éprouvette (10), cette machine comportant un poinçon mobile appliquant une charge axiale cyclique sur une face de l'éprouvette (14) perpendiculaire à l'axe du poinçon, cette éprouvette étant en appui sur une base fixe par une face opposée (12) à la première face, caractérisée en ce que la machine d'essai comporte deux appuis annulaires de rayons différents centrés sur l'axe du poinçon, appliquant la charge du poinçon ou de la base fixe sur chacune des faces opposées (12, 14) de l'éprouvette (10), la partie centrale de cette éprouvette comprenant une zone de contrainte bi-axiale (22) comportant deux surfaces parallèles, et la face (12) comportant l'appui annulaire de plus grand rayon (A), recevant sur la zone de contrainte bi-axiale (22) des jauges de déformation (20)

A Biaxial Fatigue Specimen for Uniaxial Loading

The aim of this paper is to present a novel un-notched fatigue test specimen in which a biaxial stress state is achieved using a uniaxial loading condition. This allows the problem of multi-axial fatigue to be studied using relatively common one-axis servo-hydraulic testing machines. In addition the specimen presented here is very compact and can be made using a small volume of material (100x40x4.5mm). For this specimen, the degree of biaxiality, defined by the parameter is equal to approximately 0.45. The specimen geometry was optimised using the Dang Van multi-axial fatigue criterion. In addition to use as a fatigue specimen, it has been demonstrated that the biaxial specimen presented here is also suitable for biaxial tensile tests, to determine the rupture strength of a material in a biaxial stress state. Two different materials have been investigated: The first was wrought aluminium 2024-O in the form of 5mm sheets. The second was a cast aluminium-silicon alloy AlSi7Cu0.5Mg0.3, commonly used in automotive and aeronautical applications. The fatigue strengths were determined at 2x106 cycles and at various R-ratios using a staircase procedure. For the aluminium 2024, it is shown that the biaxial stress state increases the maximum permissible first principal stress when compared to the uniaxial condition. However, in terms of the cast aluminium alloy, it has been demonstrated that this type of fatigue specimen is not suitable for materials containing casting defects, in particular micro-shrinkage pores, because the volume of material, in which the stress state is biaxial, is not large enough.The authors gratefully acknowledge the financial support of PSA – Peugeot Citroën and also that of the Conseil Général du Département de Maine-et-Loire, France

Influence des fortes contraintes hydrostatiques sur la résistance en fatigue multiaxiale

L'objectif de ce travail est de mieux comprendre l'influence de fortes contraintes hydrostatiques sur le comportement en fatigue multiaxiale à grand nombre de cycles. La démarche est analogue à celle traditionnellement mentionnée dans la littérature : analyse dissociée de l'effet de la contrainte moyenne (au moins pour la fatigue uniaxiale) et de l'effet du taux de biaxialité. Des données issues de la littérature sont utilisées afin de découpler ces deux effets et de déterminer comment les critères multiaxiaux classiques de fatigue en tiennent compte. L'attention est plus précisément portée sur les critères de Dang Van (1973) et de Papadopoulos (1999). Il apparaît que ces critères ne peuvent pas tenir compte de ces deux paramètres de chargement simultanément. Une nouvelle approche permettant de mieux prendre en compte l'effet de contraintes hydrostatiques élevées est donc proposée. Cette construction requiert l'utilisation d'un critère de fatigue multiaxiale et d'un critère de rupture ductile (Gurson

Machine d'essai en fatigue biaxiale disposant d'une éprouvette

Machine d'essai en fatigue disposant d'une éprouvette (10), cette machine comportant un poinçon mobile appliquant une charge axiale cyclique sur une face de l'éprouvette (14) perpendiculaire à l'axe du poinçon, cette éprouvette étant en appui sur une base fixe par une face opposée (12) à la première face, caractérisée en ce que la machine d'essai comporte deux appuis annulaires de rayons différents centrés sur l'axe du poinçon, appliquant la charge du poinçon ou de la base fixe sur chacune des faces opposées (12, 14) de l'éprouvette (10), la partie centrale de cette éprouvette comprenant une zone de contrainte bi-axiale (22) comportant deux surfaces parallèles, et la face (12) comportant l'appui annulaire de plus grand rayon (A), recevant sur la zone de contrainte bi-axiale (22) des jauges de déformation (20)

Simulation of the Kitagawa-Takahashi diagram using a probabilistic approach for cast Al-Si alloys under different multiaxial loads

This article describes a microstructural-based high cycle fatigue strength modelling approach applied to different cast Al-Si alloys used in an automotive context. Thank to different casting processes (gravity die casting and lost foam casting), associated with several heat treatment (T7 and Hot Isostatic Pressing-HIP), three alloys with very different microstructures have been obtained. In a vast experimental campaign undertaken to investigate the fatigue damage mechanisms governing these alloys under different multiaxial loading conditions, it was shown that the principal crack initiation mechanisms for the porosity-free alloy are either the formation of persistent slip bands (PSB) or the rupture and/or debonding of eutectic particles. For the porosity-containing alloys, the fatigue damage is always controlled by crack growth from pores. In order to take into account these fatigue damage mechanisms, a probabilistic model using a combination of the Dang Van and a modified LEFM criteria is proposed. The modified LEFM criterion is able to take into account the influence of the grain size on the threshold of the stress intensity factor. It is shown that for the porosity-free alloy, the predictions are good for combined tension-torsion loads with R = - 1. However, because the crack initiation mechanisms are not the same depending on the hydrostatic stress, the predictions are non-conservative for the uniaxial and equibiaxial tension oads with R = 0,1. For the porosity-containing alloys, the predictions are very good for the uniaxial, combined tension-torsion and equibiaxial tension loads with both R = - 1and R = 0,1. As observed experimentally, the proposed model can also predict a more pronounced effect of casting porosity for the uniaxial and combined tension-torsion loads, when compared to pure torsion loads

Fatigue behaviour of gear teeth made of case hardened steel: from competing mechanisms to lifetime variability

Jet engines gears are generally made of steel and are case-strengthened via thermochemical treatments such as carburizing or nitriding causing microstructural modifications, superficial hardening and compressive residual stresses in the surface layers. These treatments increase the resistance to cyclic loads caused by contact between teeth and by the bending loads applied to the teeth. Both of these create high stress gradients at the surface. A large number of studies concerning the effect of thermochemical treatments on fatigue resistance have been carried out for uniaxial loads (rotating bending, tension or plane bending). Most of them were undertaken using smooth specimens, which do not correctly reproduce the stress gradient at the root of the gear teeth. As a consequence, a strong dependence between the loading mode and the position of the crack initiation site is observed. The present work aims at experimentally investigating the fatigue behavior of case hardened steel with a special focus on crack initiation and growth mechanisms. A vast experimental campaign composed of two parts is undertaken. Firstly, a Single Tooth Bending Fatigue (STBF) test is carried out on gears made of 16NiCrMo13 carburized steel. The resulting Wöhler diagram shows high scatter at certain stress levels which suggests a bi-modal behavior, characterized by very different crack initiation phases. Secondly, a fatigue tests conducted on plane bending notched specimens, designed to accurately reproduce the stress gradient observed at the gear tooth root are carried out to confirm this bimodal behavior and to characterize the failure mechanisms

A two-scale finite element model for the fatigue design of large welded structures

Weld toes and weld roots of continuously welded structures subjected to cyclic loading are critical zones in terms of the fatigue resistance. The finite element method coupled with a fatigue criterion is commonly used to ensure the correct sizing and fatigue design of welded structures. However, weld geometries are often simplified or idealized to limit computational cost. In this work, a numerical two-scale approach is proposed in order to calculate a non-local multiaxial equivalent stress at the weld toe and the weld root from a global finite element shell model. The influence of the parameters of the proposed model on the stiffness behaviour is investigated for three welded structures and for different loading cases. A comparison in terms of stiffness with other models from the literature is also proposed. The results show that the stiffness behaviour is not affected by the parameters of the proposed approach and that it is the most robust model for the different geometries and loading cases studied. The variation in the non-local multiaxial equivalent stress as a function of the parameters of the proposed approach was also studied. The comparison with full solid finite element models makes it possible to define minimum values for the different parameters studied and validates the potential of the proposed approach for the fatigue design of welded structures