Schubspannungsbomben in Faserverbunden

Shear Bombs in Fibre Composites Despite an optimum external shape non‐load adapted internal fibre orientation can lead to the formation of shear cracks where crossing tension‐compression principal stress trajectories create localized shear peaks. Trees are subject to those failure because they cannot re‐arrange their fibres after wood formation. Bones can adjust their micro‐structure to changing load conditions and in this way can better control shear failure. The engineer working with fibre composites should be alert to avoid fibre arrangements not following the force flow. Localized shear zones may also form near notches similar to normal notch stresses, however they are not always situated at the contour line of the notch.     

On the possible generalizations of the Kitagawa–Takahashi diagram and of the El Haddad equation to finite life

The celebrated Kitagawa–Takahashi (KT) diagram, and the El Haddad (EH) equation, have received great attention since they define quite successfully the region of non-propagation (or the condition of self-arrest) for short to long cracks. The EH equation can be also seen as an “asymptotic matching” between the fatigue limit and the threshold of crack propagation. Above this curve, finite life is expected, since cracks propagate and eventually lead to final failure. In this paper, possible extensions of the EH equation to give the life of a specimen with a given initial crack as a function of the applied stress range, using only “asymptotic matching” equation between known regimes, namely the Wöhler SN curve (or some simplified form, like Basquin law), and the crack propagation rate curve (or just the Paris’ law). This permits an extension of the so-called “intrinsic crack” size concept in the EH equation for infinite life. The generalized El Haddad equation permits to take into account approximately of some of the known deviations from the Paris regimes, for short cracks, near the fatigue threshold or fatigue limit, or to the static failure envelope. The new equations are also plotted as SN curves, showing that power-law regimes seem very limited with many possible deviations and truncations, even when the crack propagation law has a significant power-law regime. The diagram remains partly qualitative (for example, we neglect geometric factors), and can be considered a first attempt towards more realistic maps. Particularly interesting are the cases with the Paris exponent m < 2, in which propagation tends to be very slow until very close to the toughness failure, making the maps qualitatively different.     

The fracture mechanics of finite crack extension

This paper describes a modification to the traditional Griffith energy balance as used in linear elastic fracture mechanics (LEFM). The modification involves using a finite amount of crack extension (Δa) instead of an infinitesimal extension (da) when calculating the energy release rate. We propose to call this method finite fracture mechanics (FFM). This leads to a change in the Griffith equation for brittle fracture, introducing a new term Δa/2: we denote this length as L and assume that it is a material constant. This modification is extremely useful because it allows LEFM to be used to make predictions in two situations in which it is normally invalid: short cracks and notches. It is shown that accurate predictions can be made of both brittle fracture and fatigue behaviour for short cracks and notches in a range of different materials. The value of L can be expressed as a function of two other material constants: the fracture toughness K_c (or threshold ΔK_th in the case of fatigue) and an inherent strength parameter σ₀. For the particular cases of fatigue-limit prediction in metals and brittle fracture in ceramics, it is shown that σ₀ coincides directly with the ultimate tensile strength (or, in fatigue, the fatigue limit), as measured on plain, unnotched specimens. For brittle fracture in polymers and metals, in which larger amounts of plasticity precede fracture, the approach can still be used but σ₀ takes on a different value, higher than the plain-specimen strength, which can be found from experimental data. Predictions can be made very easily for any problem in which the stress intensity factor, K is known as a function of crack length. Furthermore, it is shown that the predictions of this method, FFM, are similar to those of a method known as the line method (LM) in which failure is predicted based on the average stress along a line drawn ahead of the crack or notch.     

Analysis of non-localized creep induced strains and stresses in notches

A method for the estimation of time-dependent strains and stresses induced in notches has been developed. The aim of the method is to generate a solution for the creep strain and stress at the notch root based on the linear-elastic stress state, the constitutive law, and the material creep model. The proposed solution is an extension of Neuber’s total strain energy density rule for the case of time-independent deformation. The method was derived for both localized and non-localized creep in a notched body. Predictions were compared with finite element data and good agreement was obtained for various geometrical and material configurations in plane stress conditions.     

Constant-life diagram modified for notch plasticity

A modified constant-life Haigh diagram has been formulated to account for plasticity occurring at stress concentrations under cyclic loading at sufficiently high stress ratios. The notch plasticity is assumed to occur within a range of elastic stress concentration factors, k_t, and cycles to failure, N_f, such that plastic straining occurs only during the first cycle of constant-amplitude cycling and straining remains elastic thereafter. This condition is expected to occur in high cycle fatigue at stress concentrations of moderate k_t loaded at high stress ratio. The validity of the model is assessed by means of fatigue data from Ti–6Al–4V notched specimens having a range of k_t. The model, purposely kept simple for ease of use as a design tool, is found to capture trends in the fatigue data not predicted using traditional straight-line models on a mean stress versus alternating stress constant-life plot.     

On the use of the Theory of Critical Distances to predict static failures in ductile metallic materials containing different geometrical features

This paper summarises an attempt to use the Theory of Critical Distances (TCD) to predict static failures in notched specimens made of a commercial cold-rolled low-carbon steel. Over the last 80 years, such a theory has been successfully employed to predict both static and fatigue failures in notched components, exploring its accuracy and its reliability in different ambits of the structural integrity field. In most of these previous applications, the stress fields in the relevant region close to the notch could be assumed to be linear-elastic without much loss of accuracy. The aim of the present paper is to investigate whether this linear-elastic TCD can also be successful in predicting static failures in notched components when the final breakage is preceded by large-scale plastic deformations. Notched specimens containing different geometrical features were tested under both tensile loading and three-point bending and failures were predicted by post-processing the results of linear-elastic Finite Element Analysis (FEA). The predictions thus obtained were found to be highly accurate, falling within an error interval of about 15%, independent of specimen thickness, notch geometry and applied load type. A similar degree of accuracy was obtained when elasto-plastic stress analysis was used. This result is very interesting, because it supports the idea that the linear-elastic TCD can successfully be used in situations of practical interest, reducing the time and costs of the design process.     

A general model to estimate life in notches and fretting fatigue

Fatigue in notched specimens and fretting fatigue are two different phenomena but they have in common the existence of a stress gradient. In these cases fatigue life estimation is usually considered as a superposition of an initiation and propagation phase. One of the main problems to estimate the fatigue life is to define the crack length where one phase finishes and the other begins. The model employed in this paper combines both phases without defining a priori the separation between them. The proposed model is applied to uniaxial and multiaxial fatigue in specimens with stress gradient: a group of fretting fatigue tests with spherical and cylindrical contact and another group of tests with notched specimens. The comparison between life estimations and experimental results allows checking the validity of the model in different conditions.     

An efficient approach for shape optimization of components

The optimization problem of finding the optimal shape of a mechanical component is investigated with the aim of presenting a simple and efficient numerical approach for minimizing stress concentration factor. The proposed approach is based on finite element method in conjunction with the widely used fully stressed design criterion (or the axiom of uniform stress), i.e. for structural shape optimization, an essential requirement for optimality is the achievement of constant tangential stresses along a section of the boundary to be optimized. The design boundary is modeled by using cubic splines, which are determined by a number of control points. The optimal shape of the design boundary with constant stress is achieved iteratively by adjusting the design boundary shape based on a simple logic and algorithm. The result quality in terms of accuracy and efficiency are tested and discussed with finite element analysis examples. The approach presented has the attractive properties that it can be very simply implanted into standard finite element codes.     

A semi-analytical discretization method for the near-field analysis of unsymmetrically laminated multimaterial junctions

In the present contribution, the theoretical basics of a novel semi-analytical discretization procedure are described. The method relies on the discretization of the structural situation into an arbitrary number of sectorial elements in which adequate displacement formulations are postulated. Speaking in terms of a cylindrical coordinate system, the sectorial elements are supposed to be of infinite dimensions in the radial direction, hence the actual discretization takes place in the circumferential direction only. While linear shape functions are employed in each of the infinite sectorial elements in the circumferential direction, a set of unknown displacement functions is postulated in each of the resultant interfaces between the individual elements with respect to the radial coordinate. The principle of minimum elastic potential yields the governing Euler–Lagrange equations straightforwardly which allow for closed-form solutions for the unknown interface displacement functions. Since the method yields closed-form solutions for all state variables with respect to the radial coordinate and employs a discretization in the circumferential direction exclusively, we may actually speak of a semi-analytical methodology. Examples are presented for the near-field analysis of unsymmetrically laminated multimaterial notches. The presented semi-analytical method proves to be of high accuracy. Furthermore, while this novel discretization procedure clearly outperforms purely numerical analysis methods like FEM in terms of computational time and effort, it works with comparable accuracy which makes it very attractive for any practical application purpose with involved localization effects where reliable results need to be computed with low computational effort.     

Environment and time dependent effects on the fatigue response of an advanced nickel based superalloy

The fatigue behaviour of the nickel based superalloy RR1000 is characterised using double edge notch specimens incorporating shot peening. Evaluations were conducted at two test temperatures, 300 °C and 650 °C, employing baseline and dwell waveforms. The effects of air and vacuum environments plus prior exposure at 650 °C were also assessed. It is demonstrated that surface oxidation does not control performance at the test conditions of interest. Rather, the modification to stabilized peak and mean stresses resulting from either thermal relaxation of peened stresses or a time dependent shake down of stress under mechanical loading governs ultimate behaviour.