F. Berto

High-temperature fatigue strength of a copper–cobalt–beryllium alloy

This article summarizes the results from uniaxial tension stress-controlled fatigue tests performed at 650°C on Cu-Be specimens. Two geometries are considered: hourglass-shaped specimens and plates weakened by a central hole. The motivation of this present study is that, at the best of the authors knowledge, only a limited number of studies on copper alloys under high-temperature fatigue are available in the literature, and no results from these alloys deal with notched components. In the present contribution, after a brief review of the recent literature, material properties and experimental procedure are described. The new data from un-notched and notched specimens are summarized in the corresponding fatigue curves. By analyzing the fatigue behavior of the plates weakened by central holes, a reduction of the fatigue strength about equal to 40% at 2 million cycles can be noted, whereas the inverse slope, k, is very close to that of un-notched specimens. All fatigue data from un-notched and notched specimens are reanalyzed here in terms of the mean value of the strain energy density. The approach, successfully used to summarize fatigue data from notched specimens tested at room temperature, is extended here for the first time to high-temperature fatigue. In the plates with central holes, the strain energy density is evaluated over a finite size control volume surrounding the highly stressed zone at the hole edge. A value of the radius equal to 0.6mm seems to be appropriate to summarize all fatigue data in a quite narrow scatter band.

Brittle Failure of Graphite Weakened by V-Notches: A Review of Some Recent Results Under Different Loading Modes

The present paper summarizes some recent experimental, theoretical and numerical results on brittle fracture of isostatic polycrystalline graphite. The analyses have been carried out on V-notched samples under mixed mode (I+II), torsion and compression loading, considering various combinations of the notch tip radius, opening angle and notch tilt angle. The static strength of the considered specimens is assessed through an approach based on the strain energy density averaged over a control volume. The center of the control volume is located on the notch edge, where the principal stress reaches its maximum value. The correct orientation is obtained by a rigid rotation of the crescent-shaped volume while the size depends on the fracture toughness and the ultimate strength of the material. This methodology has been already used in the literature to analyze U- and V-shaped notches subject to mode I loading with very good results and advantages with respect to classic approaches. The results reported in this new work show, also under mixed mode loading conditions, a good agreement between experimental data and theoretical predictions.

Strain energy density to assess mode II fracture in U-notched disk-type graphite plates

The brittle fracture criterion, namely the strain energy density (SED) over a control volume, which embraces the notch edge, is utilized in the present research to assess the experimentally obtained fracture loads of several U-notched Brazilian disk (UNBD) specimens made of a type of commercial graphite under pure mode II loading. The results show that the SED criterion could successfully predict the fracture loads of graphite specimens for different notch tip radii with an average discrepancy of about ±10%. It is proved in this investigation that not only the SED criterion works well on brittle fracture of notched graphite components under pure mode I, mixed mode I/II and pure mode III loading conditions, but also under pure mode II loading.

Mode I Fracture Analysis of Polymethylmetacrylate Using Modified Energy-Based Models

The paper presents two energy-based approaches to predict the fracture trajectory and the fracture load in components containing a mode I crack. The fracture behavior of polymethylmetacrylate (PMMA) samples was investigated experimentally and theoretically for compact tension and double cantilever beam test specimens. The crack growth trajectories and the values of apparent fracture resistance in these two specimens were considerably different although both were under pure mode I loading. Two energy-based methods, i.e., the strain energy density and the averaged strain energy density criteria were modified to estimate the fracture trajectory and the fracture load in brittle materials respectively by considering the T-stress effects. The difference between the crack trajectories and the fracture resistances of different cracked specimens of the same material (PMMA) was found to be related to the magnitude and the sign of T-stress.

Tensile fracture analysis of V-notches with end holes by means of the local energy

This paper deals with investigating brittle fracture in V-notches with end holes under mode I loading. Thirty-six fracture test results, reported most recently in the literature on a new notched disk-type specimen, namely the Brazilian disk containing central VO-shaped notch made of polymethyl-metacrylate, were theoretically predicted by means of the well-known brittle fracture criterion, namely the strain energy density over a critical control volume which embraces the notch edge. A very good agreement was shown to exist between the experimental and theoretical results.

Brittle Fracture of Rounded V-Notches in Isostatic Graphite under Static Multiaxial Loading

While a large bulk of experimental results from cracked specimens of polycrystalline graphite under pure modes of loading, in particular under mode I loading, can be found in the literature, only a very limited number of tests have been carried out on notches. At the best of the author knowledge dealing with the specific case of V-notches under mixed mode loading (tension + torsion) no results can be found in the literature. With the aim to fill this lack, the problem of mixed mode (I + III) brittle fracture of polycrystalline graphite is investigated systematically here for the first time. The present study considers cylindrical specimens weakened by circumferential notches characterized by different acuities. A new complete set of experimental data is provided considering different geometrical configurations by varying the notch opening angle and the notch tip radius. The multiaxial static tests have been performed considering different values of the mode mixity ratio (i.e. the ratio between the nominal stress due to tension and that due to torsion loading). A criterion based on the local strain energy density previously applied by the same authors only to pure modes of loading is extended here to the case of tension and torsion loadings applied in combination. The proposed criterion allows a sound assessment of the fracture loads.

Mode II Brittle Fracture Assessment of Key-Hole Notches by Means of the Local Energy

Brittle fracture of key-hole notches under pure mode II loading is investigated both experimentally and theoretically. In the experimental part, a new version of the well-known Brazilian disk specimen containing a central dumbbell-shaped slit with two key-ends, called the Key-BD specimen, made of polymethyl-methacrylate (PMMA), is utilized to perform fracture experiments at room temperature for different notch lengths and various notch radii. In the theoretical part, the experimentally recorded fracture loads are predicted by means of the strain energy density (SED) averaged over a specified control volume, which embraces the notch edge. It is found that the SED criterion can successfully predict the test results.

Three-dimensional effects at the tip of rounded notches subjected to mode-I loading under cyclic plasticity

In this work, a comprehensive theoretical and numerical study on the cyclic elastic–plastic notch stress and strain distributions is carried out. In more detail, the incremental cyclic plasticity theory, already proposed by other authors to determine the actual stress and strain state arising in two-dimensional or axisymmetric notched components, is extended to the study of three-dimensional effects at the tip of rounded notches in plates of finite thickness. The analytical frame is initially validated considering a number of plane problems and later modified to consider three-dimensional effects. Different notch geometries are investigated, such as plane specimens with finite thickness weakened by circular holes, U-notches and rounded V-notches subjected to cyclic mode-I loading. Theoretical results based on the incremental cyclic plasticity theory are compared with time-consuming elastic–plastic finite element analyses carried out with a commercial finite element code showing a very satisfactory agreement. Finally, a link between the averaged strain energy density criterion and the area subtended by the hysteresis loops tied to the different stress and strain components acting at the notch tip has been investigated.

On Scale Effect in Plates Weakened by Rounded V-Notches and Subjected to In-Plane Shear Loading

It is now well-known that in plate problems with through-the-thickness cracks in-plane shear and anti-plane loadings generate coupled three-dimensional fracture modes. The dominance domain and intensity of the singular states associated with these 3D fracture modes are functions of the intensity of the primary loading (KII and KIII) and Poisson’s ratio. A similar situation takes place for V-shaped notches. However, for geometrically similar notch geometries subjected the same nominal stress the intensity of the coupled modes is also a function of the plate thickness. Despite this almost all 3D effects are currently ignored in industrial standards and fracture assessment codes. Recent theoretical and numerical studies have demonstrated that in many practical situations the intensities of the coupled fracture modes for cracks and sharp notches are not negligible and can influence fracture conditions. The current paper extends this conclusion to rounded notches. By using the finite element modelling it is demonstrated that the intensity of the stress states associated with the coupled fracture modes in a sufficiently thick plate weakened by a rounded notch can exceed the magnitude of stresses due to the primary loading. This means that the coupled modes can dominate the stress state in the vicinity of the notch root and be primary responsible for fracture initiation.

High Temperature Fatigue Tests of a Cu-Be Alloy and Synthesis in Terms of Linear Elastic Strain Energy Density

The present paper summarises the results from uniaxial-tension stress-controlled fatigue tests performed at different temperatures up to 650°C on Cu-Be specimens. Two geometries are considered: hourglass shaped and plates weakened by a central hole (Cu-Be alloy). The motivation of the present work is that, at the best of authors’ knowledge, only a limited number of papers on these alloys under high-temperature fatigue are available in the literature and no results deal with notched components.The Cu-Be specimens fatigue data are re-analyzed in terms of the mean value of the Strain Energy Density (SED) averaged over a control volume. Thanks to the SED approach it is possible to summarise in a single scatter-band all the fatigue data, independently of the specimen geometry.