P. Gallo

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.

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.

Mixed mode I/II fracture investigation of Perspex based on the averaged strain energy density criterion

In this work, some recent mixed mode I/II fracture toughness results obtained from Perspex (or polymethylmethacrylate (PMMA)) with four simple cracked specimens subjected to the conventional three-point bend loading are reanalysed based on local energy concept. Although all the mentioned samples have been tested under the same and similar mode mixities, different fracture toughness envelopes were obtained for mixed mode I/II fracture of PMMA. The averaged strain energy density (SED) criterion has been applied in the past for different types of notched specimens (including U, V, O and keyhole notches). It is shown that the mixed mode tensile-in plane shear fracture toughness data obtained from the semicircular and triangular crack type specimens are successfully predicted for sharp cracked PMMA samples using the SED criterion.

High temperature fatigue tests and crack growth in 40CrMoV13.9 notched components

The present paper addresses experimentally the high temperature fatigue of 40CrMoV13.9 steel and the effect of surface roughness on fatigue strength and crack initiation. The 40CrMoV13.9 steel is widely used in different engineering high temperature applications among which hot- rolling of metals, where, in order to assure a constant temperature, the rolls are provided with cooling channels. These are the most stressed zone of the rolls where cracks systematically initiate. In order to completely characterize the high temperature behaviour of this steel, firstly uniaxial-tension load controlled fatigue tests have been conducted at different temperatures up to 650°C. Two geometries are considered: plain specimens and plates weakened by symmetric V-notches. Subsequently, with the aim to investigate the influence of the cooling channels roughness on the high temperature behaviour and the cracks initiation, uniaxial-tension load controlled fatigue tests have been conducted on plate with central hole at the service temperature of 650°C varying the surface roughness. After a brief review of the recent literature, the experimental procedure is described in detail and the new data from un-notched and notched specimens are summarized in terms of stress range, at the considered temperatures. Finally, fatigue data from un-notched and notched specimens are re-analysed by means of the mean value of the Strain Energy Density (SED) approach extended at high temperature.

Some Considerations on the J-Integral under Elastic-Plastic Conditions for Materials Obeying a Ramberg-Osgood Law

Among the approaches available for structural analysis, the J-integral has received an excellent feedback as a fracture parameter under elastic-plastic conditions. In the literature and dealing with the crack case, it is proposed to evaluate the J-integral as a sum of elastic and plastic contributions. However, some uncertainties arise when applying this method to a Ramberg-Osgood law, especially under large scale yielding conditions.The aim of the present paper is to discuss how the J-integral evaluation can be performed for elastic-plastic cracked components. Two different non-linear behaviours have been considered for the material: the Ramberg-Osgood law and power law. Numerical and finite element results from different approaches have been accurately compared, proving that the most appropriate way to evaluate the J-integral for a material obeying Ramberg-Osgood law is to perform two finite element analyses evaluating separately the elastic contribution (through a linear elastic analysis) and the plastic contribution (through a nonlinear analysis considering power law behaviour).

Creep behavior of v-notched components

Geometrical discontinues such as notches play a significant rule in structural integrity of the components, especially when the component is subjected to very severe conditions, such as the high temperature fatigue or creep. In this paper, a generalized form of the existing notch tip creep stressstrain analysis method developed by Nunez and Glinka, is developed and extended to a wide variety of blunt V-notches. Assuming the generalized Lazzarin-Tovo solution that allows a unified approach to the evaluation of linear elastic stress fields in the vicinity of both cracks and notches is the key in getting the extension to blunt V-notches. Numerous cases have been analysed and the stress fields obtained according to the proposed method were compared with proper finite element data, showing a very good agreement.

Numerical Evaluation of T-stress under Mixed Mode Loading Through the Use of Coarse Meshes

The present paper investigates the employment of coarse meshes in evaluating the T-stress with the displacement method. Several finite element analyses have been carried out with different mesh refinements and accuracies. Mode I and mixed mode I/II loadings have been considered in finite element analyses. Under mode I loading, single and double edge notched geometries have been considered, while plate with central crack has been considerd for mixed mode loading condition. The analyses are compared with the results by the well-nown stress based approach, and showed that the displacement method permits the evaluation of the T-stress with the employment of coarse meshes. By the way, several precautions must be taken when dealing with coarse and very coarse meshes.

Investigation into the Breakdown of Continuum Fracture Mechanics at the Nanoscale: Synthesis of Recent Results on Silicon

The present contribution reviews some recent results on the experimental characterisation of the nanoscale fracture toughness of silicon by using pre-cracked specimens and alternatively the theory of critical distances (TCD). Later, the results are discussed to provide the ultimate dimensional limit of the continuum fracture mechanics at the nanoscale in the light of sophisticated discrete atomic simulations at the onset of brittle fracture. The results show that the fracture toughness of Si is independent of the scale, crystal orientation and the singular stress field length. This confirms the atomistic nature of the brittle fracture. Moreover, the continuum fracture mechanics fails below a singular stress field approaching 2 nm.