Strain Energy Density Factor Range Research Articles

CYCLIC PARAMETERS GOVERNING CRACK PROPAGATION BEHAVIOR UNDER IN-PHASE AND OUT-OF-PHASE TENSILE-TORSIONAL LOADING

Cyclic fatigue parameters governing fatigue crack propagation behavior under out-of-phase biaxial fatigue loading has been investigated considering the crack propagation direction and the growth rates. The fatigue crack was propagated by employing out-of-phase cyclic tensile-torsional loads with various phase differences to the thin-walled tubular specimen. Using two crack gages mounted near a notch, the crack propagation was measured and crack opening behaviors were monitored by unloading compliance method. The directions and growth rates of the fatigue crack propagated under respective biaxial loading conditions were examined using several cyclic fatigue parameters, including equivalent stress intensity factor range, ΔKeq, crack tip opening displacement range, ΔCTD, minimum strain energy density factor range, Δ S min . It is found that the parameters, ΔCTD and Δσθθ, max , might be useful for prediction of the crack directions and the fatigue crack growth rates were relatively well correlated with ΔKeq and Δ S min . On the other hand, the crack opening levels under in-phase loading could be relatively clearly determined, while it was ambiguous to define those under out-of-phase loading.

Investigation of Fatigue Crack Propagation in Line Pipes Containing an Angled Surface Flaw

The angled crack problem has been given special attention in the recent years by fracture mechanics investigators due to its close proximity to realistic conditions in engineering structures. In the present paper, an investigation of fatigue crack initiation and propagation in line pipes containing an inclined surface crack is presented. The inclined angle of the surface crack with respect to the axis of loading varies between 0deg and 90deg. Based on the concept of the effective stress intensity factor range Δkeff, the rate of fatigue crack propagation db∕dN is postulated to be a function of the effective strain energy density factor range ΔSeff. This concept is applied to predict the crack growth due to fatigue loading. Furthermore, the threshold condition for nongrowth of the initial crack was established and assessed based on the experimental data.

Effect of Biaxial Static Loads on Fatigue Crack Propagation Behavior under Cyclic Tensile and Torsional Loading

Fatigue crack propagation behavior under cyclic tensile or torsional loading with biaxial static loads has been investigated. Two different biaxial loading systems, i.e. cyclic tensile loading with static torsional load and cyclic torsional loading with static tensile load, were employed to thin-walled tubular specimens. The crack propagation was measured by two crack gages mounted near the notch and crack opening level was measured by unloading compliance method. The directions of the fatigue crack propagated under respective biaxial loading conditions were examined and the growth rates were evaluated by using several cyclic parameters, including equivalent stress intensity factor range, Keff, crack tip opening displacement range, CTD, minimum strain energy density factor range, Smin. Furthermore, the growth rates were evaluated by effective cyclic parameters considering crack closure. It was found that the biaxial static stress superimposed on the cyclic tensile or torsional loading tests has no influence on the propagation directions of the cracks. Furthermore, it was shown that the fatigue crack growth rates under biaixial faigue loading were well expressed by using the cyclic fatigue parameters, Keq,eff, CTDeff, Smin,eff considering crack closure effect.

Plasticity induced fatigue crack growth retardation model for steel elements reinforced by composite patch

Fatigue tests on notched steel plates reinforced by composite patch showed that the application of carbon fiber reinforced polymers (CFRP) strips with pretension of the overlays prior to bonding. This resulted in a significant amount of additional fatigue life. In particular, the pre-tension produces a compressive field in the steel plate which reduces the stress ratio that enhances crack growth retardation. The fatigue crack propagation rate is postulated to be a function of the effective strain energy density factor range. Fatigue crack growth data showed that standard crack growth retardation model cannot be used to evaluate the minimum effective stress. Hence, an ad hoc plasticity model is introduced and validated using experimental results. The proposed technique is an extension of the well know Newman’s model. The bridging effect due to the reinforcing strips is analytically modeled in order to estimate the reduction of crack opening displacement and finally the magnification of the crack growth retardation. Numerical and experimental results match well and show a significant influence of the pre-tension level on the expected fatigue crack growth rate of a reinforced steel plate.

Fatigue life prediction of the plates with an inclined surface crack

The angled crack problem has been given special attention in recent years by fracture mechanics investigators due to its close proximity to realistic conditions in engineering structures. In this paper, an investigation of fatigue crack propagation in rectangular aluminum alloy plates containing an inclined surface crack is presented. The inclined angle of the crack with respect to the axis of loading varied between 0° and 90°. During the fatigue tests, the growth of the fatigue crack was monitored using the AC potential drop technique. Based on the concept of the effective stress intensity factor range, Δ k eff, an effective strain energy density factor range, Δ S eff, is proposed in the present study. The rate of fatigue crack propagation, d b/d N, is then postulated to be a function of the effective stress intensity factor range, Δ k eff, and thus the effective strain energy density factor range, Δ S eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads.

Statistical moments of fatigue crack growth under random loading

Fracture mechanics and theory of random process are employed to derive a stochastic model of fatigue crack propagation. The uncertainties of material resistance and stress loading are introduced into the deterministic fatigue crack growth rate equation using the strain energy density factor range. The backward Fokker–Plank equation satisfying the transition probability function approximately for crack growth is derived from the stochastic averaging method. A recursive relationship for the statistical moments of time to a specific length is obtained. Given are the calculation results of mean lifetime and its standard deviation.

Influence of effective stress intensity factor range on mixed mode fatigue crack propagation

ABSTRACT The behaviour of fatigue crack propagation of rectangular spheroidal graphite cast iron plates, each consisting of an inclined semi‐elliptical crack, subjected to axial loading was investigated both experimentally and theoretically. The inclined angle of the crack with respect to the axis of loading varied between 0° and 90°. In the present investigation, the growth of the fatigue crack was monitored using the AC potential drop technique, and a series of modification factors, which allow accurate sizing of such defects, is recommended. The rate of fatigue crack propagation db/dN is postulated to be a function of the effective strain energy density factor range, ΔSeff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The mixed mode crack growth criterion is discussed by comparing the experimental results with those obtained using the maximum stress and minimum strain energy density criteria. The threshold condition for nongrowth of the initial crack is established based on the experimental data.

Mixed mode fatigue crack growth with a sudden change in loading direction

With a sudden change in the maximum load level, there will be a corresponding change in the crack driving force regardless of whether the load is applied monotonically or cyclically. The effective strain energy density factor range ΔS p,eff has been used to correlate mixed mode fatigue crack propagation where the crack growth direction is not known as an a priori. Examined in this work is a sudden change of load direction on fatigue crack growth while the load level remains unchanged. Yielding is assumed to be localized near the crack tip such that the crack growth behavior can be described adequately by the elastic stress field. Under the conditions investigated, minimal change on crack growth rates is observed. No firm conclusion could be drawn on deviation of crack path for the case considered.

FATIGUE CRACK GROWTH UNDER BIAXIAL LOADING

Fatigue crack growth under biaxial loading for long cracks subjected to low cyclic stress levels was investigated. The biaxial stress ratio λ ranging from ‐0.5 to + 1.0 was considered. The strain energy density factor range was used as the criterion for predicting the crack growth rates and crack path. The agreement between prediction and experimental results was reasonable for crack growth rates and marginal for crack paths. The investigation highlighted the inherent difficulties for crack path prediction and indicated the increased sensitivity to initial crack angle and biaxial stress ratio when the biaxial stress ratio approaches unity.

Fatigue crack growth rate in ferrite-martensite dual-phase steel

An empirical study is made on the fatigue crack growth rate in ferrite-martensite dual-phase (FMDP) steel. Particular attention is given to the effect of ferrite content in the range of 24.2% to 41.5% where good fatigue resistance was found at 33.8%. Variations in ferrite content did not affect the crack growth rate da/ dN when plotted against the effective stress intensity factor range ΔK eff which was assumed to follow a linear relation with the crack tip stress intensity factor range ΔK. A high ΔK eff corresponds to uniformly distributed small size ferrite and martensite. No other appreciable correlation could be ralated to the microstructure morphology of the FMDP steel. The closure stress intensity factor K cl , however, is affected by the ferrite content with K cl/K max reaching a maximum value of 0.7. In general, crack growth followed the interphase between the martensite and ferrite. Dividing the fatigue crack growth process into Stage I and II where the former would be highly sensitive to changes in ΔK and the latter would increase with ΔK depending on the R = σ min /σ max ratio. The same data when correlated with the strain energy density factor range ΔS showed negligible dependence on mean stress or R ratio for Stage I crack growth. A parameter α involving the ratio of ultimate stress to yield stress, percent reduction of area and R is introduced for Stage II crack growth so that the da/ dN data for different R would collapse onto a single curve with a narrow scatter band when plotted against αΔS.

Mixed mode fatigue crack growth and the strain energy density factor

The strain energy density factor S was first proposed by Sih for the prediction of the critical of the load and failure direction under monotonic, mixed mode loading condition. It seems a natural extension to apply the same concept to fatigue crack propagation. However, a close examination of the existing theory indicates that the Strain Energy Density Factor cannot logically account for the phenomena of the R-ratio effect and crack arrest. Thus, modification is necessary before the concept can be applied successfully for the prediction of mixed mode fatigue crack propagation. Based on the concept of hysteresis energy dissipation, an effective strain energy density factor range, ΔS p,eff , is proposed for the correlation of fatigue crack growth data. ΔS p,eff is consistent with the concept of crack closure. Experimental investigation indicates that it could predict the crack growth rates and trajectories.

Application of strain energy density factor to fatigue crack growth analysis

The rate of crack propagation is postulated to be a function of the strain energy density factor range, which is used to correlate the subcritical crack growth data of several different materials. Subsequently, this concept is applied to predict crack growth due to spectrum loads.

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, Δa ΔN , may involve all three stress intensity factors k 1-k 3 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 Δa 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, ΔW 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 δa ΔN relationship includes both the stress amplitude and mean stress effects.