Fatigue analysis of non-load-carrying fillet welded cruciform joints

The goal of this investigation was to study the effect of local geometrical variations of the weld on the fatigue strength. Therefore the fatigue behaviour of non-load-carrying cruciform fillet welded joint under tensile loading has been studied parametrically. Several two-dimensional (2D) finite element models of the joint were analysed using plane strain linear elastic fracture mechanics (LEFM) calculations in order to get the magnification function M_k. A maximum tangential stress criterion was used to predict the crack growth direction under mixed mode K_I-K_II conditions. The derived M_k solution was then applied both for continuous weld toe cracks and also for semi-elliptical toe cracks at the deepest point of the crack front. An experimental crack aspect ratio development curve was used for propagating semi-elliptical cracks. The as-welded condition was assumed with the result that no crack initiation period was considered and stress ranges were fully effective. The Paris crack growth law was used to predict the growth rate. The effects of weld toe radius, flank angle and weld size on the fatigue strength were systematically studied. Finally, predicted fatigue strength values corresponding to different assumed crack sizes were compared with the available test results.     

Modeling of fatigue crack growth threshold development for a microstructurally small crack

A method for predicting the fatigue crack growth threshold using finite element analysis is investigated. The proposed method consists of monitoring the plastic strain hysteresis energy dissipation in the crack tip plastic zone, with the threshold being defined in terms of a critical value of this dissipated energy. Two-dimensional plane-strain elastic-plastic finite element analyses are conducted to model fatigue crack growth in a middle-crack tension M(T) specimen. A single-crystal constitutive relationship is employed to simulate the anisotropic plastic deformation near the tip of a microstructurally small crack without grain boundary interactions. Variable amplitude loading with a continual load reduction is used to generate the load history associated with fatigue crack growth threshold measurement. Load reductions with both constant load ratio R and constant maximum stress intensity K_max are simulated. In comparison with a fixed K_max load reduction, a fixed R load reduction is predicted to generate a 35% to 110% larger fatigue crack growth threshold value.     

Analysis of the effects of compressive stresses on fatigue crack propagation rate

In this study, the effects of compressive stresses on the crack tip parameters and its implication on fatigue crack growth have been studied. Elastic–plastic finite element analysis has been used to analyse the change of crack tip parameters with the increase of the applied compressive stress level.The near crack tip opening displacements and the reverse plastic zone size around the crack tip have been obtained. The finite element analysis shows that when unloading from peak tensile applied stress to zero applied stress, the crack tip is still kept open and the crack tip opening displacement gradually decreases further with the applied compressive stress. It has been found that for a tension–compression stress cycle these crack tip parameters are determined mainly by two loading parameters, the maximum stress intensity K_max in the tension part of the stress cycle and the maximum compressive stress σ_maxcom in the compression part of the stress cycle.Based on the two parameters, K_max, and σ_maxcom, a fatigue crack propagation model for negative R ratios only has been developed to include the compressive stress effect on the fatigue crack propagation rate.Experimental fatigue crack propagation data sets were used for the verification of this model, good agreements have been obtained.     

Delamination and fatigue crack growth behavior in Fiber Metal Laminates (Glare) under single overloads

Delamination extension and fatigue crack growth behaviors under single overloads were investigated for GLARE 2-2/1-0.3 with fiber direction of 00/00. The results indicate that the stress intensity factor at the crack tip in metal layer while overload applied, K_tip,ol is a key controlling variable which influences fatigue crack growth and delamination behaviors. When K_tip,ol becomes bigger and exceeds a critical value, an obvious kink in the delamination shape is observed nearby the location of overload applied. Crack growth rate after application of overload could not return to its original level even the crack grows beyond the overload plastic zone. The reduction magnitude of the crack growth rate becomes bigger with the overload ratio (intrinsically K_tip,ol) increasing. These new results for the crack growth behavior have never been reported before, which can be well explained by the delamination extension behavior observed after overload applied.     

Experimental and finite element study on stable crack growth in three point bending

Experimental and finite element results are presented on mode I and mixed mode (involving I and II only) stable crack growth under static loading through an aircraft grade aluminium alloy (D16AT) in three point bending. The results include load-displacement diagrams, J-integrals, plastic zones, tunneling (or crack front curving), etc. During experiment a substantial amount of tunneling is observed, the extent of which increases as the extension progresses in both mode I and mixed mode. The tunneling reduces as a_o/w increases. The crack extends initially almost along a straight line at an angle with the initial crack in a mixed mode. The maximum load is observed to be as high as 1.6 times the initiation load in the whole range examined. From the finite element study it is seen that, in a mixed mode, the J-integral at the onset of extension is the lowest compared with the values at the later stages. The plastic zone size grows as the stable extension progresses; the growth is approximately the maximum along the crack extension line. The direction of initial crack extension in a mixed mode can be predicted through an elastic finite element analysis and using the criterion of maximum tangential principal stress. The study also indicates that the load-displacement diagram associated with a mixed mode stable crack growth can be predicted reasonably accurately using the criterion of crack opening angle.     

Effect of sudden load decrease on the fatigue crack growth in cold drawn prestressing steel

This paper analyzes the overload retardation effect (ORE) on the fatigue crack growth (FCG) of cold drawn prestressing steel when different loading sequences are used. The ORE is more intense for elevated load decrease or for low initial stress intensity factor (SIF) range ΔK₀. A transient stage can be observed in the Paris curve (da/dN–ΔK) when the K_maxΔK value suddenly decreases, associated with the ORE and with the evolution of the plastic zone and compressive residual stresses near the crack tip. In tests with K_max decrease, a small zone appears related to FCG initiation, with a fatigue fractography resembling the tearing topography surface (TTS) mode, and associated with a decrease of crack tip opening displacement (CTOD).     

Mixed mode fatigue crack growth predictions

This work is aimed at developing a predictive capability for the quantitative assessment of crack growth under fatigue loadings. The crack growth rate relation, $\text{Δa}\text{ΔN}$, may involve all three stress intensity factors k₁-k₃ such that the direction of crack growth may not be known in advance and must be predicted from a preassumed criterion. In principle, both the stress amplitude and the mean stress level should be included in the original expression for $\text{Δa}\text{ΔN}$.The strain energy density factor range, ΔS, is found to be a convenient parameter for predicting fatigue crack growth and can be applied expediently to examine the combined influence of crack geometry, complex loadings and material properties. Assumed is the accumulation of energy, $\text{ΔW}\text{ΔV}$, stored in an element ahead of the crack which triggers subcritical crack growth upon reaching a number of loading cycle, say ΔN. The proposed $\text{δa}\text{ΔN}$ relationship includes both the stress amplitude and mean stress effects.     

Maximum Average Tangential Stress Criterion for Prediction of the Crack Path

The concept of the average stress has been employed to propose the maximum average tangential stress (MATS) criterion for predicting the direction of fracture angle. This criterion states that a crack grows when the maximum average tangential stress in the fracture process zone ahead of the crack tip reaches its critical value and the crack growth direction coincides with the direction of the maximum average tangential stress along a constant radius around the crack tip. The tangential stress is described by the singular and non-singular (T-stress) terms in the Williams series solution. The predicted directions of fracture angle are consistent with the experimental data for the mixed mode I/II crack growth behavior of Guiting limestone.     

An accumulation damage model for fatigue fracture of ferroelectric ceramics

The accumulated plastic displacement criterion for crack propagation in traditional materials is extended to develop equations to predict the fatigue crack growth of ferroelectric ceramics subjected to combined electromechanical loads. The crack-line is perpendicular to the poling direction of the medium. An electric saturation zone and a stress saturation zone are assumed to develop at the crack tips when the medium is subjected to external electromechanical loads. This assumption makes it possible to obtain the accumulated plastic deformation in closed form. A fatigue crack growth law, which is a fourth-power function of the effective stress intensity factor, similar to the well-known Paris law, is derived. Graphical results for the effect of electric load on the effective crack tip stress intensity factor and crack growth rate are provided.     

The effect of mean stress on delay in fatigue crack growth under load stepdown

The effect of mean stress together with decreasing stress range on fatigue crack propagation behaviour in mild steel is investigated. The delay period between crack arrest and reprogation is found to be a function of the maximum stress intensity factor stepdown ration, K_2max/K_1max. Delay only occurs when this ratio is less than unity. For specimen thicknesses of 1.6 to 6.4 mm, non-propagating cracks, where the affected delay cycles are 500 000 cycles or greater, appear to occur when K_2max/K_1max has a value of approximately 0.7 and the stepdown plastic zone size is about half the initial load plastic zone size, which is approximately equal to the affected crack length.     

Effect of material plasticity on fatigue crack propagation under complex stress state

The maximum energy release rate criterion, i.e., G _max criterion, is commonly used for crack propagation analysis. However, this fracture criterion is based on the elastic macroscopic strength of materials. In the present investigation, a modification has been made to G _max criterion to implement the consideration of the plastic strain energy. This criterion is extended to study the fatigue crack growth characteristics of mixed mode cracks in steel pipes. To predict crack propagation due to fatigue loads, a new elasto-plastic energy model is presented. This new model includes the effects of material properties like strain hardening exponent n, yield strength σ_y and fracture toughness and stress intensity factor ranges. The results obtained are compared with those obtained using the commonly employed crack growth law and the experimental data.     

Fatigue notch factor and short crack propagation

This paper addresses the problem of high cycle fatigue at notches and the role of short crack propagation in the fatigue notch factor k_f. Ahead of a V-notched feature, the stress field is characterized by two parameters, i.e. the stress concentration factor k_t and the normalized notch stress intensity factor k_n. Whether fatigue strength at a given life is controlled by crack initiation (k_f = k_t) or by short crack propagation (k_f < k_t) depends on k_t, k_n and the material resistances to crack initiation and to short crack propagation. The analysis accounts for the effects of notch acuity, notch size, material and fatigue life on the fatigue notch factor k_f. It opens the door to a new method for predicting fatigue life using two S-N curves for a given material; one being measured from a smooth specimen, the other from a severe V-notch.     

Limitations of elastic definitions in Al-Si-Mg cast alloys with enhanced plasticity: linear elastic fracture mechanics versus elastic-plastic fracture mechanics

Linear elastic fracture mechanics describes the fracture behavior of materials and components that respond elastically under loading. This approach is valuable and accurate for the continuum analysis of crack growth in brittle and high strength materials; however it introduces increasing inaccuracies for low-strength/high-ductility alloys (particularly low-carbon steels and light metal alloys). In the case of ductile alloys, different degrees of plastic deformation precede and accompany crack initiation and propagation, and a non-linear ductile fracture mechanics approach better characterizes the fatigue and fracture behavior under elastic-plastic conditions.To delineate plasticity effects in upper Region II and Region III of crack growth an analysis comparing linear elastic stress intensity factor ranges (ΔK_el) with crack tip plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) is presented. To compute plasticity corrected stress intensity factor ranges (ΔK_pl), a new relationship for plastic zone size determination was developed taking into account effects of plane-strain and plane-stress conditions (“combo plastic zone”). In addition, for the upper part of the fatigue crack growth curve, elastic-plastic (cyclic J based) stress intensity factor ranges (ΔK_J) were computed from load-displacement records and compared to plasticity corrected stress intensity factor ranges (ΔK_pl). A new cyclic J analysis was designed to compute elastic-plastic stress intensity factor ranges (ΔK_J) by determining cumulative plastic damage from load-displacement records captured in load-control (K-control) fatigue crack growth tests. The cyclic J analysis provides the true fatigue crack growth behavior of the material. A methodology to evaluate the lower and upper bound fracture toughness of the material (J_IC and J_max) directly from fatigue crack growth test data (ΔK_FT(JIC) and ΔK_FT(Jmax)) was developed and validated using static fracture toughness test results. The value of ΔK_FT(JIC) (and implicitly J_IC) is determined by comparing the plasticity corrected elastic fatigue crack growth curve with the elastic-plastic fatigue crack growth curve. A most relevant finding is that plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) are in remarkably good agreement with cyclic J analysis results (ΔK_J), and provide accurate plasticity corrections up to a ΔK corresponding to J_IC (i.e. ΔK_FT(JIC)). Towards the end of the fatigue crack growth test (above ΔK_FT(JIC)) when plasticity is accompanied by significant tearing, the cyclic J analysis provides a more accurate way to capture the true behavior of the material and determine ΔK_FT(Jmax). A procedure to decouple and partition plasticity and tearing effects on crack growth rates is given.Three cast Al-Si-Mg alloys with different levels of ductility, provided by different Si contents and heat treatments (T61 and T4) are evaluated, and the effects of crack tip plasticity on fatigue crack growth are assessed. Fatigue crack growth tests were conducted at a constant stress ratio, R = 0.1, using compact tension specimens.     

Environmental effects on fracture resistant and biaxial fatigue design of aircraft structures

This paper discusses the two interrelated fields of crack initiation and crack propagation by presenting analytical techniques for calculating fatigue damage in biaxially stressed structures along with determining safe inspection intervals for contained crack growth.The equivalent stress concept is used to derive a set of uniaxial stresses that produce the same amount of fatigue damage as the biaxial stress exposure. The distortion energy concept serves as the basis for combining alternating principal stresses by translating the uniaxial SN curves for zero mean stress into a family of concentric ellipses. The major axis bisects the principal stress axes for isotropic materials with invariant directional fatigue performance. The intercept of these ellipses with the maximum alternating principal stress axis defines the equivalent alternating stress at various cyclic lives.Empirical procedures are given for treating problems with varying principal stress directions and areas with directional dependent fatigue performance.The Goodman diagram relates alternating stresses and mean stresses at any constant cyclic life. If two uniaxial Goodman diagrams are constructed on each reference axis, a three-dimensional body can be visualized which intercepts the zero alternating stress plane in a shape identical to that described by the applicable static load criterion. The equivalent mean stress concept is based on the existence of a similarly shaped closed surface at any value of alternating stress. The intercept of this surface boundary with the maximum mean stress axis is the equivalent mean stress.Crack growth rates and residual strength of structure are important items since it is necessary to consider the possible existence of cracks. Static failsafety consists of contained crack growth for reasonable lengths of time and back-up structure providing alternate load paths. The stress intensity factor $\text{K}$, reflecting the distribution of stress in cracked structure, is the basis for computing crack growth. Baseline crack growth data for several material toughnesses and environmental exposures is required for fracture analysis. The method employed consists of calculating stress intensities for various crack lengths in the structure, these primarily being a function of geometry and applied stress distribution. The crack growth curves are constructed by integrating the baseline data for the appropriate corrosive exposure with additional factors applied to allow for scatter in growth rates and load magnitudes.     

The fatigue crack growth rate and crack opening displacement in 18G2A-steel under tension

In the paper, the results of crack tip opening displacement (CTOD) and crack opening displacement (COD) in place of crack initiation as well as the fatigue crack growth rate in higher strength steel are presented. The investigation were carried out on flat specimens with central notch under constant amplitude tensile fatigue loading at stress ratio R = 0.2 and different value of the stress σ_max. The test results showed that with growth of crack length l grew values of the CTOD and COD. In the work, it was proposed calculation of the CTOD value on basis various dependence of plastic zone radius on crack tip.     

Mode I fatigue crack growth under biaxial loading

This paper is centred on the role of the T-stress during mode I fatigue crack growth. The effect of a T-stress is studied through its effect on plastic blunting at crack tip. As a matter of fact, fatigue crack growth is characterized by the presence of striations on the fracture surface, which implies that the crack grows by a mechanism of plastic blunting and re-sharpening (Laird C. The influence of metallurgical structure on the mechanisms of fatigue crack propagation. In: Fatigue crack propagation, STP 415. Philadelphia: ASTM; 1967. p. 131–68 [8]). In the present study, plastic blunting at crack tip is a global variable ρ, which is calculated using the finite element method. ρ is defined as the average value of the permanent displacement of the crack faces over the whole K-dominance area. The presence of a T-stress modifies significantly the evolution of plastic deformation within the crack tip plastic zone as a consequence of plastic blunting at crack tip. A yield stress intensity factor K_Y is defined for the cracked structure, as the stress intensity factor for which plastic blunting at crack tip exceeds a given value. The variation of the yield stress intensity factor was studied as a function of the T-stress. It is found that the T-stress modifies significantly the yield point of the cracked structure and that the yield surface in a (T, K_I) plane is independent of the crack length. Finally, a yield criterion is proposed for the cracked structure. This criterion is an extent of the Von-Mises yield criterion to the problem of the cracked structure. The proposed criterion matches almost perfectly the results obtained from the FEM. The evolution of the yield surface of the cracked structure in a (T, K_I) plane was also studied for a few loading schemes. These results should develop a plasticity model for the cracked structure taking into account the effect of the T-stress.     

Effect of crack closure on non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, some authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle were investigated. It was demonstrated that: (i) LEFM concepts are applicable to the problem under study; (ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; (iii) the ΔK_eff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; and (iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level. Therefore the crack closure concept seems to be valid. Additionally, the curves of crack tip parameters against stress intensity factor range obtained without contact may be seen as master curves.     

A parametric fracture mechanics study of welded joints with toe cracks and lack of penetration

The existing design rules give quite general guidelines to the fatigue assessment of different types of welded joints. The goal of this investigation was to give designers some tools, which would allow more precise assessment of the effect of dimensional variations on the fatigue strength. Therefore the fatigue behaviour of 12 common types of welded joints has been studied parametrically. Two-dimensional (2D) finite element models of the joint were made and evaluated using plane strain linear elastic fracture mechanics (LEFM) calculations. The as-welded condition was assumed with the result that no crack initiation period was considered and stress ranges were fully effective. A maximum tangential stress criterion with the Paris’ crack growth law was used to predict the growth rate and direction of root and toe cracks under mixed mode K_I-K_II conditions. The effects of weld size and joint dimension ratios on the fatigue strength were systematically studied. In addition to tensile loading, bending and combined tension/bending moment loading in both directions are examined for positive and negative mean stress.     

A fracture mechanics model for the analysis of micro-pitting in regard to lubricated rolling–sliding contact problems

A computational model is presented for the analysis of micro-pitting in regard to lubricated rolling–sliding contact problems. This model assumes the appearance of an initial microcrack on the contact surface due to the mechanical or thermal treatment of the material, and as a consequence of an on-going process in early the stage of exploitation. The discretised model of the contacting mechanical elements is subjected to normal loading (Hertzian contact pressure), tangential loading (friction between contacting surfaces) and internal pressure to the crack surfaces. Crack propagation is predicted as follows: (1) using modified maximum tangential stress criterion, which takes into account the influence of stress intensity factors K_I and K_II, T-stress, stress on the crack’s surface caused by lubricant pressure inside the crack, and the critical distance ahead of the crack tip and (2) the classical maximum tangential stress criterion, which only takes into account the influence of the stress intensity factors K_I and K_II. The stress intensity factor based on these two criteria is then used in a short crack growth theory to determine the fatigue life of an initial crack to extent up to micro-pit. The developed model is applied to a real spur gear pair.     

MIXED-MODE FRACTURE MECHANISMS NEAR THE FATIGUE THRESHOLD OF AISI 316 STAINLESS STEEL

Abstract— Near threshold, mixed mode (I and II), fatigue crack growth occurs mainly by two mechanisms, coplanar (or shear) mode and branch (or tensile) mode. For a constant ratio of ΔK_I/ΔK_II the shear mode growth shows a self-arrest character and it would only start again when ΔK_I and ΔK_II are increased. Both shear crack growth and the early stages of tensile crack growth, are of a crystallographic nature; the fatigue crack proceeds along slip planes or grain boundaries. The appearance of the fracture surfaces suggest that the mechanism of crack extension is by developing slip band microcracks which join up to form a macrocrack. This process is thought to be assisted by the nature of the plastic deformation within the reversed plastic zone where high back stresses are set up by dislocation pile-ups against grain boundaries. The interaction of the crack tip stress field with that of the dislocation pile-ups leads to the formation of slip band microcracks and subsequent crack extension. The change from shear mode to tensile mode growth probably occurs when the maximum tensile stress and the microcrack density in the maximum tensile plane direction attain critical values.