Comparative study and link between mesoscopic and energetic approaches in high cycle multiaxial fatigue

Multiaxial fatigue analysis can be categorized into several viewpoints, i.e. empirical formulae, methods based on stress invariants, critical plane approaches, models using averages of stress quantities and energetic considerations. The aim of this paper is not to survey the current state of knowledge concerning multiaxial fatigue but to critically examine two endurance criteria so as to prove that a direct link can be established between them. The first of the two methods, proposed by Papadopoulos, has been built by exploring the fatigue of metals from the mesoscopic scale, that is from the scale of the metal grains of a metallic aggregate. The localized plastic strains developping in some less favourably oriented crystals is considered to be the main cause of fatigue crack nucleation. According to relationships between macroscopic and mesoscopic quantities, this model is finally expressed in terms of the usual macroscopic stresses relative to an elementary material volume. The second approach proposed by Froustey and Lasserre is an energetic based criterion. It has been deduced from experimental observations concerning multiaxial endurance limit and states that crack initiation occurs as soon as the total strain energy density exceeds a critical value. This paper shows that the critical value of the accumulated mesoscopic plastic strain used by Papadopoulos to characterize the endurance limit can be estimated with the global strain energy density at the macroscopic scale. Indeed, it is demonstrated that when dealing with in-phase or out-of-phase synchronous sinusoidal constant amplitude loadings, a single analytical formulation of these criteria can be written either with stress quantities or with energetic ones describing thus the same physical phenomenon. The mean stress influence is discussed; the predictions of the two approaches are similar when the material remains quasi elastic. Another important result concerns the phase difference of the stress tensor components. Very few approaches are able to predict the independence of the fatigue strength on the phase difference between normal and shear stresses. The two proposed criteria reflect this phenomenon which has been experimentally observed for many metals subjected to combined bending-torsion loading. Nevertheless, this independence with regard to the phase shift is no more effective when dealing with some biaxial stress systems with two normal stresses. In this case the two models are consistent with the experimental results since they show a marked influence of the phase difference

Low velocity impact response and damage of laminate composite glass fibre/epoxy based tri-block copolymer

International audienceTwo types of laminate composites made of glass fibre/epoxy matrix (EPO_FV) and glass fibre/epoxy modified tri-block copolymer (Nanostrength) matrix (EPONS_FV) were manufactured by compression moulding. Some AFM investigations have been done to identify the Nanostrength dispersion in the epoxy matrix and some DMA analyses have been performed, at different frequencies, to understand the frequency or the strain rate sensitivity of both composites. Compared to EPO_FV, EPONS_FV exhibits a significant frequency/strain rate sensitivity. Impact resistance of the composite was investigated by means of low velocity impact tests. The low velocity impact results indicate that the addition of Nanostrength leads to the improved impact resistance and an increase in absorbed energy, especially at high impact energy level. SEM observations, Performed on ion polished samples, reveal the presence of micro-cracks for both composites. Micro-cracks consist of a coalescence of fibre matrix de-bonding. It was also observed that EPONS_FV contains a lower density of micro-cracks compared to EPO_FV, confirming the fact that the composite with Nanostrength absorbs more energy by Nanostrength micelles cavitation

Impact response of thick composite plates under uniaxial tensile preloading

This work focuses on the impact response of composite plates 5 mm thick subjected to uniaxial tension preload. Laminated carbon/epoxy with quasi-isotropic stacking sequence ([0/45/90/-45]2)S samples were used. Doehlert-type design of experiments was proposed to investigate the influence of both preload and impact energy on impact composite responses. Deformation, varying from 300 to 3000 micro-strain, was imposed thanks to a preload device designed for this purpose. Impacts were generated using a home made drop tower. Imposed impact energy was varying from 30 to 214 J. Post-impact damage was characterized by both non-destructive (ultrasound) and destructive (deply) techniques. Influence of the preloading on delamination areas (total and projected) was quantified and found sensitive to the preloading

Comportement à l'impact des composites fibres de verre/Epoxy modifié copolymère à bloc.

Epoxy resins are widely used in the design of fibre composite materials. This increasing use finds its reason in the fact that these materials have excellent mechanical and thermal properties. Playing on its chemical composition and curing speed, it’s possible to vary the mechanical properties from the extreme flexibility to high rigidity. However, the inherent toughness of a highly crosslinked epoxy is relatively low. It therefore seems desirable for high impact resistance applications, to improve the toughness, without affecting the other usual properties of this polymer. Recent studies have shown a significant improvement in impact resistance of epoxy in the presence of block copolymers. Our work aims to investigate the effect of triblock copolymer-based acrylate (Nanostrength) on the impact resistance of glass / epoxy composite. An experimental device, called "drop tower" is used to perform impact tests on composites with or without Nanostrength. Dynamic mechanical analyses (DMA) were conducted, first to characterize the effect of addition of Nanostrength on the thermomechanical properties, but also to establish a correlation between thermomechanical properties and impact resistance. Different observation tools, such as optical observation, scanning electron microscopy (SEM) and atomic force microscopy (AFM) were used to visualize the material damages. Adding Nanostrength in epoxy leads to the improvement of impact resistance of the composite material. A slight decrease in the storage modulus and glass transition temperature have been observed. Microscopic observations shown that the different failure modes of the composite are mainly delamination, fibres breakage and matrix cracking. It was also observed that the presence of Nanostrength role as cracks deflect

Low velocity impact response and damage of laminate composite glass fibre/epoxy based tri-block copolymer

Two types of laminate composites made of glass fibre/epoxy matrix (EPO_FV) and glass fibre/epoxy modified tri-block copolymer (Nanostrength) matrix (EPONS_FV) were manufactured by compression moulding. Some AFM investigations have been done to identify the Nanostrength dispersion in the epoxy matrix and some DMA analyses have been performed, at different frequencies, to understand the frequency or the strain rate sensitivity of both composites. Compared to EPO_FV, EPONS_FV exhibits a significant frequency/strain rate sensitivity. Impact resistance of the composite was investigated by means of low velocity impact tests. The low velocity impact results indicate that the addition of Nanostrength leads to the improved impact resistance and an increase in absorbed energy, especially at high impact energy level. SEM observations, performed on ion polished samples, reveal the presence of micro-cracks for both composites. Micro-cracks consist of a coalescence of fibre matrix de-bonding. It was also observed that EPONS_FV contains a lower density of micro-cracks compared to EPO_FV, confirming the fact that the composite with Nanostrength absorbs more energy by Nanostrength micelles cavitation

Comparative study and link between mesoscopic and energetic approaches in high cycle multiaxial fatigue

Multiaxial fatigue analysis can be categorized into several viewpoints, i.e. empirical formulae, methods based on stress invariants, critical plane approaches, models using averages of stress quantities and energetic considerations. The aim of this paper is not to survey the current state of knowledge concerning multiaxial fatigue but to critically examine two endurance criteria so as to prove that a direct link can be established between them. The first of the two methods, proposed by Papadopoulos, has been built by exploring the fatigue of metals from the mesoscopic scale, that is from the scale of the metal grains of a metallic aggregate. The localized plastic strains developping in some less favourably oriented crystals is considered to be the main cause of fatigue crack nucleation. According to relationships between macroscopic and mesoscopic quantities, this model is finally expressed in terms of the usual macroscopic stresses relative to an elementary material volume. The second approach proposed by Froustey and Lasserre is an energetic based criterion. It has been deduced from experimental observations concerning multiaxial endurance limit and states that crack initiation occurs as soon as the total strain energy density exceeds a critical value. This paper shows that the critical value of the accumulated mesoscopic plastic strain used by Papadopoulos to characterize the endurance limit can be estimated with the global strain energy density at the macroscopic scale. Indeed, it is demonstrated that when dealing with in-phase or out-of-phase synchronous sinusoidal constant amplitude loadings, a single analytical formulation of these criteria can be written either with stress quantities or with energetic ones describing thus the same physical phenomenon. The mean stress influence is discussed; the predictions of the two approaches are similar when the material remains quasi elastic. Another important result concerns the phase difference of the stress tensor components. Very few approaches are able to predict the independence of the fatigue strength on the phase difference between normal and shear stresses. The two proposed criteria reflect this phenomenon which has been experimentally observed for many metals subjected to combined bending-torsion loading. Nevertheless, this independence with regard to the phase shift is no more effective when dealing with some biaxial stress systems with two normal stresses. In this case the two models are consistent with the experimental results since they show a marked influence of the phase difference

Low-velocity impact tests on carbon/epoxy composite laminates: A benchmark study

Low-velocity impacts (LVI) on composite laminates pose significant safety issues since they are able to generate extended damage within the structure, mostly delaminations and matrix cracking, while being hardly detectable in visual inspections. The role of LVI tests at the coupon level is to evaluate quantities that can be useful both in the design process, such as the delamination threshold load, and in dealing with safety issues, that is correlating the internal damage with the indentation depth. This paper aims at providing a benchmark of LVIs on quasi-isotropic carbon/epoxy laminates; 2 laminates are tested, 16 and 24 plies and a total of 8 impact energies have been selected ranging from very low energy impacts up to around 30 J. Delamination threshold loads, shape and extension of délaminations as well as post-impact 3D measurements of the impacted surface have been carried out in order to characterize the behavior of the considered material system in LVIs. The analysis of test results relevant to the lowest energies pointed out that large contact force fluctuations, typically associated to delamination onset, occurred but ultrasonic scans did not reveal any significant internal damage. Due to these unexpected results, such tests were further investigated through a detailed FE model. The results of this investigation highlights the detrimental effects of the dissipative mechanisms of the impactor. A combined numericale-experimental approach is thus proposed to evaluate the effective impact energies

Review of Intermediate Strain Rate Testing Devices

Materials undergo various loading conditions during different manufacturing processes, including varying strain rates and temperatures. Research has shown that the deformation of metals and alloys during manufacturing processes such as metal forming, machining, and friction stir welding (FSW), can reach a strain rate ranging from 10−1 to 106 s−1. Hence, studying the flow behavior of materials at different strain rates is important to understanding the material response during manufacturing processes. Experimental data for a low strain rate of 103 s−1 are readily available by using traditional testing devices such as a servo-hydraulic testing machine and the split Hopkinson pressure bar method, respectively. However, for the intermediate strain rate (101 to 103 s−1), very few testing devices are available. Testing the intermediate strain rate requires a demanding test regime, in which researchers have expanded the use of special instruments. This review paper describes the development and evolution of the existing intermediate strain rate testing devices. They are divided based on the loading mechanism; it includes the high-speed servo-hydraulic testing machines, hybrid testing apparatus, the drop tower, and the flywheel machine. A general description of the testing device is systematically reviewed; which includes the working principles, some critical theories, technological innovation in load measurement techniques, components of the device, basic technical assumption, and measuring techniques. In addition, some research direction on future implementation and development of an intermediate strain rate apparatus is also discussed in detail.This project received funding from the European Union’s Marie Skłodowska–Curie Actions (MSCA) Innovative Training Networks (ITN) H2020-MSCA-ITN-2017 under the grant agreement No. 76497

Strain rate effect on the mechanical properties of a glass fibre reinforced acrylic matrix laminate. An experimental approach

The aim of this study is to evaluate the effect of the loading rate on the mechanical properties and damage mechanisms of a Glass/Elium150 laminate composite. Quasi-static indentation (QS) and low energy dynamic impact (DYN) tests which simulate lifetime structural loadings (dropped tool, gravel impacts, …) are lead. A specific experimental approach is developed to compare results of both experiments. The effect of the loading rate on the structural response (stiffness, dissipated energy) of the composite is highlighted. The numerous damage mechanisms involved in the collapse of the material are observed at a microscopic scale using both optical and scanning electron microscopy (SEM). Finally an intra-laminar crack propagation mechanism is described based on post-mortem observations at ply scale to explain the formation of interlaminar crack

Comportement à l'impact des composites fibres de verre/Epoxy modifiée copolymères à blocs

Les résines Epoxy sont très utilisées dans la conception des matériaux composites à fibres longues. Cette utilisation croissante trouve sa raison dans le fait que ce matériau possède d’excellentes propriétés mécaniques et thermiques. En jouant sur sa composition chimique et la vitesse de cuisson, il est possible de faire varier ses propriétés mécaniques, de l’extrême flexibilité à une rigidité très élevée. Cependant la ténacité inhérente d’un Epoxy fortement réticulé est relativement faible. Il semble donc désirable, pour des applications de tenue aux chocs, d’améliorer la ténacité, sans pourtant affecter les autres propriétés usuelles de ce polymère. Des études récentes ont montré une amélioration significative de résistance à l’impact de l’époxy en présence des copolymères à blocs. Notre travail vise précisément à étudier l'effet du copolymère tribloc à base d’acrylate (Nanostrength) sur la résistance aux chocs du composite verre / époxy. Un dispositif expérimental, dénommé « tour de chute » est utilisé pour effectuer des tests d'impact sur les composites avec et sans Nanostrengths. Des analyses dynamiques mécaniques (DMA) ont été menées pour, non seulement caractériser l'effet de l’ajout de Nanostrength sur les propriétés thermomécaniques, mais également pour établir une corrélation entre propriétés thermomécaniques et résistance à l’impact. Différents outils d'observation, tels que l'observation optique, la microscopie électronique à balayage (MEB) et la microscopie à force atomique (AFM) ont été utilisés pour visualiser l’endommagement du matériau. L’ajout de Nanostrength dans l'époxy conduit à une amélioration de la résistance au choc du matériau composite. Une diminution du module de conservation et de la température de transition vitreuse ont également été observées. Les observations au microscope attestent que les différents modes de ruine du composite sont essentiellement du délaminage, la rupture des fibres et de la fissuration de matrice. Il a été aussi observé que la présence de Nanostrength a pour rôle de dévier les fissures