RICERCA ITALIANA     

Methods for fatigue resistance evaluation of notched structural components under multiaxial loading

Università degli Studi di Parma

Abstract

The proposed Research Project aims at developing design and assessment methodologies for civil and mechanical structural components with severe notches under multiaxial fatigue loading. In particular, constant and variable amplitude multiaxial loading, both in-phase and out-of-phase, will be considered.

The life prediction models which will be developed by the Research Units will average either the stresses or the strain energy in a material volume located in the most highly stressed zone. These theoretical models will represent an extension of what has already been proposed by some of the researchers involved in the present Project. The theoretical predictions will be compared with experimental data available in the literature or obtained from tests performed by some of the Research Units. As is well-known, the root of a notch is a preferential site for initiation and growth of a fatigue defect. Therefore, it is essential to analyse the effect of the multiaxial fatigue loading on crack initiation, crack growth and fatigue resistance of the notched structural components being examined. Such phenomena will be analysed by employing fatigue and fracture mechanics concepts. For medium/low-cycle fatigue (finite life), the notch induces stress components that, for strain hardening materials, can overcome the yield stress. In those conditions, the values of the local loading ratio R are not much lower than the unity. As a consequence, fatigue strength could be obtained by extrapolating the results of standard tests on smooth specimens at low R ratios. Indeed, the global plastic strain of the specimens makes rather difficult to obtain information on the resistance at high R ratios through standard fatigue tests and specimens.

The theoretical models developed by the Research Units will be applied to real structural components, such as bridge girders, transmission shafts, welded joints. Furthermore, experimental as well as numerical activities will be carried out in order to validate and calibrate the above models.

The experimental activity will be performed on axi-symmetric specimens, subjected to combined tensile and torsional loadings, and simple welded structural components, subjected to complex loading conditions with stresses both in-phase and out-of-phase. The nucleation of the so-called "technical defect" (significant from an engineering point of view) will be examined in depth, and the ratio between the crack nucleation phase and the crack propagation phase will be evaluated as a function of the geometry of the structural component, the loading conditions, the stress level.

The numerical activity will be focused on the development of methodologies to examine real structures, by also considering welded structures. Such methods should make it possible to identify and separate global effects from local ones. Generally, global effects will be analysed by means of simple beam or "thin shell" FE (finite element) models in order to obtain the input parameters for evaluating local effects. Such local effects will be examined by means of more refined 3D FE models, suitable to account for the stress concentration in the critical zones (for example, near the notches) of the structural components. <<<

Principal Investigator

Andrea CARPINTERI Università degli Studi di PARMA

Research Objectives

The proposed Research Project aims at developing design and assessment methodologies for civil and mechanical structural components with severe notches under multiaxial fatigue loading.

As a first step, the Research Project aims at collecting information available in the literature related to the design methodologies of notched structural components subjected to multiaxial fatigue. In such a way, it will be increased the amount of data available by the researchers involved in this Project.

Several contributions on this subject have recently been presented at the international scientific community by the above researchers. In particular, high-cycle fatigue (close to fatigue limit conditions) has been analysed. Moreover, the criterion by Susmel and Lazzarin and that by Carpinteri et al. (see Section 2.2 below) have already been systematically verified by using several experimental data available in the literature, related to smooth or blunt-notched specimens.

In the presence of stress concentration due to severe notches, the above criteria need some "ad hoc" modifications. As a matter of fact, the fatigue behaviour does not follow a point criterion, but it is rather controlled by what occurs in a small but finite volume of material surrounding the most highly stressed zone. The Research Project aims at also extending the two above criteria from high-cycle fatigue to finite life, i.e. medium/low-cycle fatigue, by highlighting their accuracy degrees and validity ranges.

Since the root of a notch is a preferential site for initiation and growth of a fatigue defect, it is essential to analyse the effects of the multiaxial fatigue loading on the crack growth and the fatigue resistance of the notched structural components being examined. Such effects will be analysed by employing fatigue and fracture mechanics concepts, by also proposing methods to evaluate a mathematical relationship between the conventional stress-intensity factor (SIF) and the notch stress-intensity factor (N-SIF, for notched structures). In order to determine some parameters describing the crack behaviour, an approach based on the weight function method will be applied. Some researchers involved in the present Project have already used such a method for examining the behaviour of oblique edge cracks in unnotched structural components.

The present Research Project will consist of theoretical, experimental and numerical activities, and will be in contact with the ESIS (European Structural Integrity Society) TC3 Technical Committee on "Fatigue of Engineering Materials and Structures" (chaired by Professor Andrea Carpinteri from the Parma Research Unit). In particular, the main topics of the Project "Energy-based approach to multiaxial fatigue using the critical plane" being developed by the TC3 Sub-Committee "Multiaxial Fatigue" will be also considered.

In more detail, theoretical studies to extend a multiaxial fatigue criterion (proposed by the researchers of the Parma Research Unit) based on the critical plane approach will be carried out. Particular emphasis will be laid in the principal stress direction variation due to non proportional multiaxial fatigue loading. The main aims of the Parma Research Unit are:
- extension of the above criterion to variable amplitude loading by the formulation of an appropriate method for the damage accumulation and cycles counting;
- extension to severely notched structural components by means of a non-local approach.

The theoretical developments proposed will be supported by experimental data obtained by the Research Units involved. Concerning to the experimental activity, the Padua Research Unit will perform fatigue tests on steel axis-symmetric specimens, both smooth and severely V notched (with a notch tip radius lower than or equal to 0.5 mm). Such tests will be carried out by using an MTS biaxial testing machine, available at the Department of Management Engineering of Vicenza. Two types of steel (C40 steel, AISI 416 stainless steel) commonly used for transmission shaft will be used. The specimens will be tested under tensile, torsion and mixed tensile/torsion loading. Both in-phase and out-of-phase loading will be considered. The main aims of the experimental programme are:
- to carefully analyse and describe of the nucleation phase of fatigue cracks, specifying the "technical crack" size as a function of the material and loading conditions;
- to verify an energetic criterion for fatigue strength prediction of structural components with sharp notches subjected to multiaxial fatigue.

The experimental activity by the Ferrara Research Unit will be focused on welded structural components subjected to complex constant amplitude stresses, both in-phase and out-of-phase. Traditional manual arc welding techniques and a typical structural steel will be used. As is well-known, welded joints made with such techniques are characterised by extremely small toe radius and, for this reason, a criterion based on the stress-intensity factors by also considering the notch effect ("Notch Stress-Intensity Factor", N-SIF) could successfully be applied. The aims of this activity are:
- evaluation of the nucleation and propagation phases of the fatigue crack as a function of the structural component geometry and loading level;
- extension of the point method, the line method and the bi-parametric Wöhler curve (Susmel and Lazzarin, 2002) to multiaxial fatigue.

With respect to the numerical activity, the aims of the Ferrara Research Unit are as follows:
- N-SIF computation of welded connections subjected to multiaxial loadings;
- development of methods for N-SIF estimation in real structural components subjected to multiaxial loadings.

Many notched structural components can experience overloads that can induce local plastic strain at the notch root. This problem is complex as it involves many aspects of the fatigue resistance. The notch induces stress components that can overcome, for strain hardening materials, the yield stress. In those conditions, local R-ratios not much lower than the unit can be expected. As a consequence, it appears rather questionable to obtain fatigue strength properties by extrapolating the results from standard tests on smooth specimens at low R ratios. Indeed, the global plastic strain of the specimens makes rather difficult to obtain information on the resistance at high R ratios with standard fatigue tests and specimens. The Pisa Research Unit aims at studying this aspect of the fatigue resistance of notched structures by a combined numerical-experimental approach that includes the design, the conduction and the interpretation of fatigue tests on notched specimens, by also carrying out elastic-plastic analyses using the finite element method.

The activity of the Trento Research Unit will be focused on the definition as well as the validation of computational methods for studying the propagation of cracks emanating from sharp notches. The activity is complementary with respect to the principal aims of the other Research Units. The approach that is intended to be used is based on the application of the weight function method for determining the fracture mechanics parameters necessary to analyse the behaviour of a fatigue crack subjected to general loading histories. The main aim is to apply the above computational technique to the problem of a semiplane with a sharp notch having different values of depth and angular aperture, by considering a crack with a variable length and inclination at the notch root. <<<

First Results

Updating of the state of the art in the field of the Research Project, improvement of the available database. The validity range and the degree of accuracy of some life prediction methods already available for high-cycle fatigue will be examined. Planning of the research activities of the Research Units involved in the present Project.Strength and life prediction models for multiaxial fatigue in the presence of notches and stress concentrations as well as for finite life. Additional multiaxial fatigue data for the different structural components and loading conditions analysed. Results obtained from the numerical analyses performed.Validity range of the developed models and degree of accuracy in life and strength predictions. Procedures for the application of the models to complex civil and mechanical structural components. Final reports of the Research Project. <<<

Timescale

24 months

National and international background

Since civil and mechanical structural components frequently work under multiaxial fatigue loading, the problem of the multiaxial fatigue assessment has long been investigated by several researchers [1]. The analysis of the state of the art shows that the approaches vary mainly as a function of the fatigue life, and are different for low-cycle fatigue and high-cycle fatigue. The most popular low-cycle fatigue life estimation techniques are based on a strain approach (see, for example, the critical plane-based criteria proposed by Socie and co-workers [2-5], Brown and Miller [6], and Wang and Brown [7] as well as the energy criterion introduced by Ellyin [8-10]). These criteria are sometimes extended also to high-cycle fatigue, the plastic strain contribution being negligible. On the other hand, all the high-cycle multiaxial fatigue criteria are based on the stress components only. This is true, for example, for the mesoscopic approach-based criteria proposed by Dang Van [11] or Papadopoulos [12,13] and for the critical plane-based criteria due to McDiarmid [14,15], Matake [16] and Findley [17]. All these methods are well-known to the scientific community and a discussion about them is, obviously, out of the aims of the present Research Project proposal.

Other "stress-based criteria", recently presented in the literature, have mainly been developed by the researchers who are proposing this Project.

In January 2002 Susmel and Lazzarin presented a method suitable for estimating high-cycle fatigue strength under multiaxial loading conditions [18]. The physic interpretation of the fatigue damage was based on the theory of the cyclic deformation in single crystals. Such a theory was also used to identify the stress components which can be considered really significant for the crack nucleation and growth in the so-called Stage I. The underlying idea is that crack initiation is Mode II (sliding) governed, according to the critical plane approach due to Socie and Marquis [19]. Fatigue life estimates were carried out by means of a modified Wöhler curve which can be applied to both smooth and blunt-notched structural components, subjected to either in-phase or out-of-phase loads. The modified Wöhler curve plots the fatigue strength in terms of the maximum macroscopic shear stress amplitude, the reference plane - where such an amplitude has to be evaluated - being thought of as coincident with the fatigue micro-crack initiation plane. The position of the fatigue curve depends on the stress component normal to such a plane and also on the phase angle between the stress components. About 450 experimental data taken from the literature were used to check the accuracy of the above method under high-cycle multiaxial loading conditions.

In recent years, the critical plane approach has been studied by Carpinteri et al., and a new criterion has been proposed [20-23] which correlates the critical plane orientation with the weighted mean principal stress directions. In more detail, a theoretical procedure which is deemed to account for the changes of the principal stress axes under fatigue loading has been developed to determine the averaged principal stress directions through the weight function method. Appropriate weight functions have been proposed in order to take into account the main factors influencing the fatigue fracture behaviour. Then, the weighted mean direction of the maximum principal stress is used to predict the orientation of the fracture plane, and to deduce the critical plane where to carry out the fatigue failure assessment. Finally, such an assessment is performed by considering a nonlinear combination of the maximum normal stress and the shear stress amplitude acting on the critical plane.

One of the aims of the present Project is to extend the method by Susmel and Lazzarin and that by Carpinteri et al. from the fatigue limit condition to finite life regime. Generally speaking, when a structural component is subjected to complex cyclic loadings, both in-phase and out-of-phase loading [24], fatigue crack initiation (Stage 1) is usually fracture Mode II (sliding) dominated, whereas the subsequent crack growth phase (Stage 2) is Mode I (opening) governed. The amount of each stage principally depends on both the material properties and the stress distribution in a fatigue process zone [25] and, in a notched structural component, the Stage 1 decreases as the value of the theoretical stress concentration factor increases. These aspects will carefully be considered in this Project, when extending the above criteria from high-cycle fatigue to medium/low-cycle fatigue.

In the presence of a small fillet radius and, hence, of high stress concentration effects, it is well-known that it is no longer the theoretical stress concentration factor which rules the fatigue strength of a structural component but rather a mean value of the stress in a fatigue process zone. An assessment of the fatigue reduction factor Kf needs the knowledge of the notch sensitivity index, which can be evaluated by means of some well-known expressions due to Neuber, Peterson and Heywood. In order to assess the fatigue limit of notched structural components subjected to multiaxial fatigue, some critical distance methods have recently been proposed, the so-called point method and the line method [26-30], based on the linear elastic fracture mechanics and capable of fatigue limit predictions with an error of about 20%. Both models involve the El-Haddad-Topper parameter a0 [31], often called "intrinsic crack" in the technical literature. In particular, the effective stress is evaluated at a0/2 distance from the notch tip when the point method is applied, whereas it is evaluated by means of an integration of the maximum principal stress over a line of length 2a0 when the line criterion is applied.

In parallel, when the notch tip radius tends to zero, the "Notch Stress-Intensity Factors" have been proposed in the technical literature to predict the strength of structural components made of brittle materials [32-35], and to examine the initiation phase of cracks in structural components and welded joints made of conventional materials [36,37]. Subsequently, the N-SIF criterion has also been used to predict the total fatigue life, at least in those cases where the greater part of the structural component life is spent in the nucleation and propagation of micro-cracks inside the zone governed by an asymptotic stress field [38-40]. As a matter of fact, a mathematical relationship exists between the conventional stress-intensity factor (SIF) pertaining to the Linear Elastic Fracture Mechanics and the N-SIF [39,41]. On the basis of the structural volume concept due to Neuber, the averaged strain energy density (total or deviatoric) has been evaluated in a control volume surrounding the tip of a sharp V-shaped notch. Such an energy density is a function of the N-SIFs [42]. The use of a strain energy based parameter instead of a stress based parameter makes easy the bridging from 2-dimentional problems (governed by Mode I and Mode II factors) to 3-dimensional problems (governed by Mode I, Mode II and Mode III), and allows us to apply a unified approach to both low-cycle and high-cycle fatigue [43]. It is also important to remark [44] that a relationship exists between energetic criteria and two "mesoscopic" criteria proposed by Dan Van and by Papadopoulos, respectively [11-13].

Sharply notched engineering structural components under fatigue loading conditions are likely to undergo plastic deformations at the notch root, at least during the first cycles of loading [45]. Due to interaction between external loading and plastic stress redistribution, actual cycle parameters (in particular R-ratio) can be quite different from those typical of the external loading history. In addition, there are indications concerning a relevant influence of the plastic zone size on the initiation and growth process of short cracks at the notch root [45]. Among sharply notched structural components, an important category is that of high-strength threaded connections (e.g. special bolts for automotive constructions, conical threaded connections for oil drilling batteries, threaded connections of tendons for large civil or offshore structures, etc.) [46,47]. Such components often experience fatigue loading histories characterised by the above phenomena.

The study of the onset and initial propagation of fatigue cracks emanating from notches is very important to evaluate the fatigue life of a structural component. For this type of problem, the weight function method [48] can be a very efficient tool to determine the stress-intensity factors, in particular if, as for the fatigue life analysis, many fracture mechanics evaluations have to be carried out as the crack grows during the structural component life, with complex variations of loading. Furthermore, the method has been proved to be particularly powerful also for the evaluation of the crack opening displacement (COD), thus allowing to account for possible conditions of partial crack closure, quite usually observed for cracks at notches, due to the local plastic deformation induced by the stress concentration at the notch root [45], or due to the effect of possible surface treatments [49].

In conclusion, the main aim of the Research Project is to study the multiaxial fatigue behaviour of severely notched structural components, i.e. for small values of the notch tip radius. Some criteria for smooth or blunt-notched structural components, already developed by the researchers involved in the Project [18, 20-23], will be extended to the above case. Further, criteria proposed in literature [36-42] for sharp V-shaped notches, till now limited to uniaxial fatigue only, will be extended to multiaxial fatigue. The criteria proposed in the present Project will be compared, verified and validated. Great attention will also be paid to their extension and application to real structural components of civil or mechanical interest like bridge girders, transmission shafts, welded joints. <<<