On the Dominant Role of Crack Closure on Fatigue Crack Growth Modeling

Abstract Crack closure is the most used mechanism to model thickness and load interaction effects on fatigue crack propagation. But assuming 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 ϪK op , not on ⌬K. But this assumption would imply that the normal practice of using da/dN×⌬K curves measured under plane-stress conditions (without considering crack closure) to predict the fatigue life of components working under planestrain could lead to highly non-conservative errors, because the expected fatigue life of "thin" (plane-stress dominated) structures could be much higher than the life of "thick" (plane-strain dominated) ones, when both work under the same stress intensity range and load ratio. However, crack closure cannot be used to explain the overload-induced retardation effects found in this work under plane-strain, where both crack arrest and delays were associated to an increase in ⌬K eff . These results indicate that the dominant role of crack closure in the modeling of fatigue crack growth should be reviewed

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 well establishedmechanical 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 theloading, 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

Incorporation of Mean/Maximum Stress Effects in the Multiaxial Racetrack Filter

This work extends the Multiaxial Racetrack Filter (MRF) to incorporate mean or maximum stress effects, adopting a filter amplitude that depends on the current stress level along the stress or strain path. In this way, a small stress or strain amplitude event can be filtered out if associated with a non-damaging low mean or peak stress level, while another event with the very same amplitude can be preserved if happening under a more damaging high mean or peak stress level. The variable value of the filter amplitude must be calculated in real time, thus it cannot depend on the peak or mean stresses along a load event, because it would require cycle identification and as so information about future events. Instead, mean/maximum stress effects are modeled in the filter as a function of the current (instantaneous) hydrostatic or normal stress along the multiaxial load path, respectively for invariantbased and critical-plane models. The MRF efficiency is evaluated from tension-torsion experiments in 316L stainless steel tubular specimens under non-proportional (NP) load paths, showing it can robustly filter out nondamaging events even under multiaxial NP variable amplitude loading histories. KEYWORDS. Multiaxial racetrack filter; Mean/peak stress effects; Nondamaging events; Multiaxial loads

Application of the Moment Of Inertia method to the Critical-Plane Approach

The Moment-Of-Inertia (MOI) method has been proposed by the authors to solve some of the shortcomings of convex-enclosure methods, when they are used to calculate path-equivalent ranges and mean components of complex non-proportional (NP) multiaxial load histories. In the proposed 2D version for use with critical-plane models, the MOI method considers the non-proportionality of the projected shear-shear history on each candidate plane through the shape of the load path, providing good results even for challenging non-convex paths. The MOI-calculated path-equivalent shear stress (or strain) ranges from each counted load event can then be used in any shear-based critical-plane multiaxial fatigue damage model, such as Findley’s or Fatemi-Socie’s. An efficient computer code with the shear-shear version of the MOI algorithm is also provided in this work. KEYWORDS. Multiaxial fatigue; Non-proportional loadings; Equivalent ranges; Critical-Plane Approach

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

A model to quantify fatigue crack growth by cyclic damage accumulation calculated by strip-yield procedures

Elber's hypothesis that DeltaKeff can be assumed as the driving force for fatigue crack growth (FCG) is the basis for strip-yield models widely used to predict fatigue lives under variable amplitude loads, although it does not explain all load sequence effects observed in practice. To verify if these models are indeed intrinsically better, the mechanics of a typical strip-yield model is used to predict FCG rates based both on Elber's ideas and on the alternative view that FCG is instead due to damage accumulation induced by the cyclic strain history ahead of the crack tip, which does not need or use DeltaKeff ideas. The main purpose here is to predict FCG using the cyclic strains induced by the plastic displacements calculated by strip-yield procedures, assuming there are strain limits associated both the with the FCG threshold and with the material toughness. Despite based on conflicting principles, both models can reproduce quite well FCG data, a somewhat surprising result that deserves to be carefully analyzed

A two-step multiaxial racetrack filter algorithm for non-proportional load histories

The recently proposed multiaxial racetrack filter (MRF) is able to deal with general non-proportional multiaxial load histories. While only requiring a single user-defined scalar filter amplitude, the MRF is able to synchronously eliminate non-damaging events from any noisy multiaxial load history without changing the overall shape of its original path, a necessary condition to avoid introducing errors in fatigue damage assessments. The MRF procedures are optimized here by the introduction of a pre-processing “partitioning” step on the load history data, which selects candidates for the reversal points in a robust partitioning process, highly increasing the filter efficiency and decreasing its computational time. The improved MRF is evaluated through the fatigue analyses of over-sampled tension-torsion data measured in 316L stainless steel tubular specimens under non-proportional load paths

On short cracks that depart from elastoplastic notch tips

The behavior of short cracks that depart from elastoplastic notch tips is modeled to estimate the stresses required to initiate and to propagate cracks in notched structural components, and to evaluate the size of tolerable crack-like defects under general loading conditions. This analysis can model both fatigue and environmentally assisted cracking problems; can evaluate notch sensitivity in both cases; and can as well be used to establish design or acceptance criteria for tolerable non-propagating crack-like defects in such cases. The growth of short cracks is assumed driven by the applied stresses and by the stress gradient ahead the notch tip, and supported by the material resistances to crack initiation and to long crack propagation by fatigue or EAC. In the elastoplastic case, the stress gradient ahead of the notch tip is quantified by a J-field to consider the short crack behavior. The tolerable short crack predictions made by this model are evaluated by suitable fatigue and EAC tests of notched specimens specially designed to start nonpropagating cracks from the notch tips, both under elastic and elastoplastic conditions

Stress Intensity Factor Equations for the Evolution of Surface and Corner Cracks to Through Cracks

Part-through surface or corner 2D cracks are commonly found in structural components, even because practically all fatigue cracks tend to start this way. It is a reasonable hypothesis to model them assuming the shape of their fronts is approximately an elliptic arc, as supported by many fractographic observations. But their transition to a 1D through-crack, an important issue in many practical applications, is normally not properly addressed in fatigue life predictions. Although experimental results reveal that the frontier of surface cracks essentially retain their elliptical shape as they gradually grow into a through-crack, it is usual to assume they are immediately transformed into a through-crack when their depth reaches the cracked component thickness. This crude approximation may create a large jump in stress intensity values, leading to excessively conservative fatigue crack growth predictions, or else the crude shape jump hypothesis may induce false overload events that can much affect fatigue crack growth retardation models, leading to inadmissible non-conservative life predictions. To minimize such problems, an improved model to describe the transition of 2D surface cracks to 1D through-cracks is proposed and verified by crack propagation tests in two different materials, 4340 steel and polycarbonate (PC). Moreover, fatigue life predictions based on this improved model are compared with experimental results

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