Jaime Tupiassú Pinho de Castro

On the dominant role of crack closure on fatigue crack growth modeling

AbstractCrack closure is the most used mechanism to model thickness and load interaction effects on fatigue crack propagation. Butassuming it is the only mechanism is equivalent to suppose that the rate of fatigue crack growth da/dN is primarily dependent on K eff =K max K op , not on K. But this assumption would imply that the normal practice of using da/dN× K curves measuredunder plane-stress conditions (without considering crack closure) to predict the fatigue life of components working under plane-strain could lead to highly non-conservative errors, because the expected fatigue life of “thin” (plane-stress dominated) structurescould be much higher than the life of “thick” (plane-strain dominated) ones, when both work under the same stress intensity rangeand load ratio. However, crack closure cannot be used to explain the overload-induced retardation effects found in this work underplane-strain, where both crack arrest and delays were associated to anincrease in K eff . These results indicate that the dominantrole of crack closure in the modeling of fatigue crack growth should be reviewed.2003 Elsevier Ltd. All rights reserved.

Fatigue life prediction of complex 2D components under mixed-mode variable amplitude loading

Accurate residual fatigue life predictions under variable amplitude (VA) loading are essential to maximize the time between the required inspections in defect-tolerant structures. However, this is not a trivial task for real structural components, in which cracks may change direction as they grow due to mixed-mode loading. Such curved crack paths can be predicted using finite element (FE) techniques, but this approach is not computationally efficient to predict the residual life, because it would require timeconsuming remeshing of the entire structure after each rain-flow counted load event under VA loading. In this work, a two-phase methodology that is both precise and cost-effective is applied to solve this problem. First, the fatigue crack path and stress intensity factors KI and KII are calculated in a specialized (global) FE program using fixed crack increments, requiring only relatively few remeshing steps. Then, an analytical expression is fitted to the calculated KI(a) values, where a is the length along the crack path, and exported to a companion fatigue design program to predict the crack propagation life by the local approach, considering load interaction effects such as crack retardation or arrest after overloads. This two-phase methodology is experimentally validated by fatigue tests on compact tension specimens, modified with holes positioned to attract or to deflect the cracks.  2003 Elsevier Ltd. All rights reserved.

An Evaluation of Elber-Type Crack Retardation Models

In this work, a review of plasticity induced crack closure is presented, along with models proposed to quantify its effect on the subsequent crack growth rate. The stress state dependence of crack closure is discussed. Overloadinduced retardation effects on the crack growth rate are considered, based on the crack closure idea, and improvements to the traditional models are proposed to account for crack arrest and crack acceleration after compressive underloads. Using a general-purpose fatigue design program, the models and the proposed modifications are compared with experimental results from various load spectra, and with simulated histories illustrating their main features.

A multiaxial incremental fatigue damage formulation using nested damage surfaces

Multiaxial fatigue damage calculations under non-proportional variable amplitude loadings still remains a quite challenging task in practical applications, in part because most fatigue models require cycle identification and counting to single out individual load events before quantifying the damage induced by them. Moreover, to account for the non-proportionality of the load path of each event, semi-empirical methods are required to calculate path-equivalent ranges, e.g. using a convex enclosure or the MOI (Moment Of Inertia) method. In this work, a novel Incremental Fatigue Damage methodology is introduced to continuously account for the accumulation of multiaxial fatigue damage under service loads, without requiring rainflow counters or path-equivalent range estimators. The proposed approach is not based on questionable Continuum Damage Mechanics concepts or on the integration of elastoplastic work. Instead, fatigue damage itself is continuously integrated, based on damage parameters adopted by traditional fatigue models well tested in engineering practice. A framework of nested damage surfaces is introduced, allowing the calculation of fatigue damage even for general 6D multiaxial load histories. The proposed approach is validated by non-proportional tensiontorsion experiments on tubular 316L stainless steel specimens.

On the Errors Induced by the Hookean Modeling of Nominal Stresses in the eN Method

The traditional eN procedures are inconsistent when modeling nominal stresses by Hooke’s law and the stresses and strains at the critical notch root by Ramberg-Osgood’s equation, since the material is the same at both regions. When the nominal stresses are not substantially smaller than the yielding strength SY, the predicted hysteresis loops at the notch root can be significantly non-conservative. In fact, when the nominal stresses are in the order of SY, the Hookean model can predict stresses and strains at the notch root that are smaller than the nominal ones, a clear nonsense. To avoid this problem, it is mandatory to use Ramberg-Osgood to model both the nominal and the critical stresses and strains. However, this approach is not trivial to implement, especially when complex loads are involved. In this work, the methodology required to warrant correct numerical predictions of the critical loops under high nominal loads are discussed.

Comparison between SSF and Critical-Plane models to predict fatigue lives under multiaxial proportional load histories

Materials can be classified as shear or tensile sensitive, depending on the main fatigue microcrack initiation process under multiaxial loadings. The nature of the initiating microcrack can be evaluated from a stress scale factor (SSF), which usually multiplies the hydrostatic or the normal stress term from the adopted multiaxial fatigue damage parameter. Low SSF values are associated with a shear-sensitive material, while a large SSF indicates that a tensile-based multiaxial fatigue damage model should be used instead. For tension-torsion histories, a recent published approach combines the shear and normal stress amplitudes using a SSF polynomial function that depends on the stress amplitude ratio (SAR) between the shear and the normal components. Alternatively, critical-plane models calculate damage on the plane where damage is maximized, adopting a SSF value that is assumed constant for a given material, sometimes varying with the fatigue life (in cycles), but not with the SAR, the stress amplitude level, or the loading path shape. In this work, in-phase proportional tension-torsion tests in 42CrMo4 steel specimens for several values of the SAR are presented. The SSF approach is then compared with critical-plane models, based on their predicted fatigue lives and the observed values for these tension-torsion histories. KEYWORDS. Multiaxial fatigue life prediction; Critical-plane approach; Polynomial stress scale factor approach.

Is notch sensitivity a stress analysis problem

Semi–empirical notch sensitivity factors q have been widely used to properly account for notch effects in fatigue design for a long time. However, the intrinsically empirical nature of this old concept can be avoided by modeling it using sound mechanical concepts that properly consider the influence of notch tip stress gradients on the growth behavior of mechanically short cracks. Moreover, this model requires only wellestablished mechanical properties, as it has no need for data-fitting or similar ill-defined empirical parameters. In this way, the q value can now be calculated considering the characteristics of the notch geometry and of the loading, as well as the basic mechanical properties of the material, such as its fatigue limit and crack propagation threshold, if the problem is fatigue, or its equivalent resistances to crack initiation and to crack propagation under corrosion conditions, if the problem is environmentally assisted or stress corrosion cracking. Predictions based on this purely mechanical model have been validated by proper tests both in the fatigue and in the SCC cases, indicating that notch sensitivity can indeed be treated as a stress analysis problem.

Fatigue Life Predictions for L-Shaped Cracks

This paper focuses on the modeling of fatigue lives of L-shaped cracks obtained by unusual crack tests performed in plates first loaded under tensile loads and then under out-of-plane pure bending loads. To ensure life predictions accuracy, the paper compares two different methodologies. The first uses three points from the measured crack fronts and the corresponding stress intensity factors obtained by numerical simulations. The fatigue crack front is assumed to advance during growth in each point in the normal direction. Fatigue lives are calculated for each one of the three paths. The second methodology uses only one point of the crack front on the bottom surface of the plate to evaluate fatigue life. The results of fatigue life from both approaches are compared and discussed.

Issues With Multiaxial Fatigue Assessment in the ASME Boiler and Pressure Vessel Code

This work analyzes the applicability of the ASME Boiler and Pressure Vessel Code procedures to calculate fatigue crack initiation under multiaxial stresses and/or strains, in particular when caused by non-proportional loads that lead the principal directions at the critical point to vary with time, e.g. due to outof-phase bending and torsion loads induced by independent sources. Classic uniaxial fatigue damage models are usually inappropriate for analyzing multiaxial loads, since they can generate highly inaccurate predictions. Moreover, it is shown that the ASME procedures can lead to non-conservative results for non-proportional load histories. INTRODUCTION Service loads can be applied on one or on several points of a structural component. They can be generated by only one or by multiple sources, coherent or not. In general, such loads cause bending, torsion, normal, and/or shear efforts which, when combined, can (and usually do) generate multiaxial strains and stresses at the critical point(s) of the component. Multiaxial fatigue deals with the initiation and/or the propagation of fatigue cracks under such general conditions. Multiaxial fatigue load histories can be proportional or non-proportional (NP). They are proportional when the principal axes of the stresses and strains induced by them, and thus their maximum-shear planes, remain fixed during their entire duration. On the other hand, NP loads induce principal stress/strain directions that change in time (1). Consider for instance a tension-torsion problem where a shaft is loaded by a normal stress x(t) in the x direction combined with a shear stress xy(t), where t stands for time. In this case, the principal stresses 1 and 2 and the angle 1 between 1 and the x axis are given by 2 x x 2 1,2 xy 2 2              and xy 1 1 x 2 (t) 1 (t) tan 2 (t)            (1) When the shear and normal stresses are proportional, the ratio xy(t)/x(t) and the angle 1(t) remain fixed for all time t, thus this simple multiaxial loading history is proportional. If xy(t)/x(t) and hence 1(t) vary with time, then the loading is non-proportional. The relative degree of non-proportionality of any multiaxial load history is quantified by its so-called nonproportionality factor 0  FNP  1, with FNP  0 standing for a proportional load history and FNP  1 for a fully NP history. If all stress and strain components are periodic and have the same frequency, they can also be classified as in-phase or out-of-phase. Figure 1 shows in-phase as well as 90 and 180 out-of-phase tension-torsion load histories. Both the in-phase and the 180 out-of-phase loadings have a constant xy(t)/x(t) ratio, so they are proportional histories with FNP  0. The 90 out-of-phase tension-torsion loading, on the other hand, always results in a NP history, with the FNP value depending on the ratio between the shear and normal amplitudes. It is usually accepted (1) that, in tension-torsion histories, the maximum value FNP  1 is achieved for sinusoidal 90 out-of-phase loadings with equal amplitudes for x and xy3, when the von Mises stress 2 2 x xy 3    remains constant along the load path.

EVALUATION OF THE DRIVING FORCE IN FATIGUE CRACK GROWTH, IN PLANE STRAIN AND PLANE STRESS STATE TESTS, UNDER CONSTANT ΔK

This work presents a series of experiments of Fatigue Crack Growth (FCG), which are intended to provide evidence about the main parameter controlling this phenomenon, whereas still no agreement about this, since the Paris ́ theory is based on the principle that FCG is controlled by the ΔK and the Elber ́s theory says that the driving force is ΔKeff. For the development of the experiments, some DC(T) specimens were machined with two different thicknesses: 2 and 30 mm to perform FCG tests in plane stress and plane strain state, respectively. Besides this, all FCG tests were carried out with a constant ΔK e Kmax, measuring the strain with a StrainGage bonded on the back face of the specimen and seven Strain-Gages located on the crack growth path. The data needed to measure the crack opening load, and the ΔKeff, were collected through a program developed in Labview. Finally, the data postprocessing was carried out based on the ASTM standards and several articles of recognized authors in this field, in order to compare the two positions with the experimental data, and this way conclude which is the most consistent theory with the observed behavior.