T.H. Topper

Prediction of non propagating cracks

Abstract An explanation for non propagating fatigue cracks is presented based on the criterion that once the value of a particular strain intensity factor reduces to the threshold value for the material the crack should stop. Predicted lengths of these cracks based on solutions for the intensity factor are in good agreement with the experimental data. Intensity factor trends for cracks in notches are shown to vary from an initial decrease to a minimum value followed by an increase and eventual convergence with the trend for the equivalent long crack for sharp notches to the blunt notch curves that continuously increased during their approach to the long crack trend. The type of trend exhibited by a given notch depends both on notch geometry and notch size. In blunt notches the maximum value of the threshold stress for crack propagation is at initiation. However, for sharp notches the peak value of the threshold stress vs crack length curves shifts to a finite length. Stresses above the initiation level but below this peak stress level result in fatigue cracks which start but do not propagate to failure. Predicted values of the fatigue limit stresses for a variety of sizes in a circular and an elliptical notch are in good agreement with experimental results.

Long-Term Performance of Corrosion-Damaged Reinforced Concrete Beams

Research is needed to clarify the interaction between the degree of corrosion, the corrosion crack width, and the load carrying capacity in the presence of a sustained load in reinforced concrete (RC) beams having well-anchored steel reinforcement. This article reports on a study that investigated the combined effect of corrosion and sustained loads on the structural performance of nine RC beams (each measuring 152 x 254 x 3200 mm). One beam was tested as a virgin while eight beams were exposed to accelerated corrosion for up to 310 days using an impressed current technique. Four beams were corroded under a sustained load that corresponded to approximately 60% of the yield load of the virgin beam. The four remaining beams were kept unloaded during the corrosion exposure. Test results showed that the presence of a sustained load and associated flexural cracks during corrosion exposure significantly reduced the time to corrosion cracking and slightly increased the corrosion crack width. The presence of flexural cracks during corrosion exposure initially increased the steel mass loss rate and, consequently, the reduction in the beam strength. As time progressed, no correlation between the reduction in the beam strength and the presence of flexural cracks was observed.

Changes in crack-opening stress after underloads and overloads in 2024-T351 aluminium alloy

Abstract A variable-amplitude block-loading history consisting of high, near-yield-stress, underloads or compression-tension overloads followed by constant-amplitude small cycles was used to examine underload and compression-tension overload induced reductions in crack closure and the subsequent build-up of crack-opening stress to its steady-state level in a 2024-T351 aluminium alloy. Special attention was given to the near-threshold region, where the crack growth rate was less than 10−9 m cycle−1 The crack-opening stress level and the crack growth rate were measured for four different R-ratios of the small cycles following underloads and compression-tension overloads using a 900 power short focal length optical microscope. The crack-opening stress levels were measured at frequent intervals after the underload and compression-tension overload applications until the crack-opening stress returned to a steady-state level. The crack-opening stress build-up was then described by an empirical formula in terms of the ratio of the difference between the instantaneous crack-opening stress of the small cycles (Sop) and the post-underload and compression-tension overload crack-opening stress levels (Sopol), and the difference between the steady-state crack-opening stress of the small cycles (Sopss) and the post-underload and compression-tension overload crack-opening levels, ( S op − S opol ) (S opss −S opol ). Effective stresses calculated using this formula were used to predict crack growth rates. The formulas predictions showed good agreement with experimentally measured crack growth rates. For simplicity, both underloads and compression-tension overloads will be referred to as overloads in the remainder of this paper.

Analytical Model to Predict Nonlinear Flexural Behavior of Corroded Reinforced Concrete Beams

No suitable analysis is presently available to predict the flexural behavior of corroded reinforced concrete (RC) beams. This article presents a new analytical model that predicts the nonlinear flexural behavior of both corroded and newly constructed reinforced concrete beams. The authors first review previous studies in this field, noting deficiencies that required a new model. They then explain how in the proposed model, the deflection of a reinforced concrete beam is calculated from the elongation of the steel reinforcement between flexural cracks rather than from the curvatures of beam sections. This model accounts for the reduction in the steel area and the change in bond strength at the steel-to-concrete interface caused by corrosion. The effect of a loading-unloading cycle on the flexural behavior is also taken into account. The authors also propose a new bond stress-slip model that accounts for the change in bond strength due to corrosion. A comparison of the model’s predictions with experimental results showed that the model accurately predicts the load-deflection curves of both corroded and newly constructed beams.

Engineering Analysis of the Inelastic Stress Response of a Structural Metal Under Variable Cyclic Strains

Inelastic stress response under strain cycling conditions is analyzed in terms of the three important governing phenomena, namely, memory of prior history, cyclic hardening or softening, and cyclic mean stress relaxation.Independent formulations to describe these respective features consist of a set of hysteresis rules, a set of transient stress-strain relations, and an empirical exponential model. A new approach to accurately describe the hysteresis loop shape characteristics is also presented. While strain amplitude and number of cycles are used as the primary variables influencing cyclic hardening, softening, and relaxation, the effect of other variables on these features and hence their mutual interactions are observed to be small. Therefore, as a first approximation it is postulated that independent formulations based on constant amplitude test data are applicable to spectrum loading situations. Computer based models resulting from this analysis are suitable for predicting the cyclic stress-strain and fatigue response of ductile structural metals and also provide a basis for developing general flexural response models.

Fatigue of cast aluminium alloys under constant and variable-amplitude loading

Abstract Three cast aluminium materials, Al 206, Al 319 and Al 390, were fatigue tested under constant- and variable-amplitude loading. A stress ratio of −1 was used for the constant-amplitude tests. The variable-amplitude load history consisted of underloads followed by constant-amplitude small cycles. The stress ratio and the number of the constant-amplitude small cycles following an underload were adjusted so that the crack did not close and remained fully open for all the small cycles. Underloads reduced the fatigue strength of the alloys by 66–77%. A crack growth analysis based on a fracture mechanics approach was used to model the fatigue behaviour of the cast aluminium material under constant- and variable-amplitude loading. The crack growth analysis was based on an effective strain-based intensity factor, elastic and plastic notch strain calculations based on Neubers formula, and a reference crack growth rate curve obtained during closure-free crack growth. In modelling the fatigue life behaviour of cast aluminium the flaws were modelled as circular notches having the same diameter as the flaws. The notches were assumed to be edge notches, which represents the flaw location with the most detrimental effect on fatigue life. Fatigue life predictions were in good agreement with experimental results. The fatigue life behaviour for an ideal cast material free of flaws was also predicted using the same model for an unnotched specimen. The cast material was then hipped (the material was subjected to a high pressure at high temperature and then slowly cooled) to eliminate internal laws. The hipped material showed an increase in fatigue strength of almost 40% under constant-amplitude loading with R = −1, which was in good agreement with the results predicted by the model.

The effective stress range as a mean stress parameter

Abstract This investigation examines the hypothesis that variations in the crack opening stress level of short cracks can account for the observed variations in fatigue strength with mean stress under constant-amplitude cyclic loading. Support for the hypothesis is provided by the experimental data generated for a 2024-T351 aluminium alloy and a SAE 1045 steel. Based on the observed variations in crack opening stress with mean stress an effective stress range is postulated as a mean stress parameter. The effective stress range successfully reduces the fatigue data for all levels of mean stress to a unique fatigue-life curve for each material.

Prediction of crack-opening stress levels for 1045 as-received steel under service loading spectra

Abstract A crack growth analysis based on a fracture mechanics approach was used to model the fatigue behavior of as-received 1045 steel specimens for three load spectra scaled to various maximum stress range levels. The crack growth analysis was based on an effective strain-based intensity factor, a crack growth rate curve obtained during closure-free loading cycles, and a local notch strain calculation based on Neuber’s rule. The crack-opening stresses were modeled assuming that the crack-opening stress when it is not at the constant amplitude steady-state level for a given stress cycle builds up as an exponential function of the difference between the current crack-opening stress and the steady-state crack-opening stress of the given cycle unless this cycle is below the intrinsic stress range for crack growth or the maximum stress in the cycle is below zero in which cases the crack-opening stress does not change. The crack-opening stress model was implemented in a fatigue notch model and the fatigue lives of the notched annealed 1045 steel specimens under the three different load spectra scaled to several maximum stress levels were estimated. The average measured crack-opening stresses for the various histories and levels were within between 8 and 13% of the average calculated crack-opening stresses. The fatigue life predictions based on the modeled crack-opening stresses were in good agreement with the experimentally obtained fatigue data. The averages of the measured crack-opening stresses and those calculated using the model were nearly the same for all the histories examined. When these average crack-opening stresses were used in the life prediction model they gave predictions as good as those obtained by modeling crack-opening stress on a cycle by cycle basis. The use of a crack-opening stress level corresponding to the cycle causing a reduction to a crack-opening stress reached for 1/200 of the cycles in the history gave a conservative estimate of average crack-opening stress for all the histories.

Fatigue Flexural Behavior of Corroded Reinforced Concrete Beams Repaired with CFRP Sheets

This study investigated the flexural behavior of corroded steel reinforced concrete beams repaired with carbon-fiber-reinforced polymer (CFRP) sheets under repeated loading. Thirty beams ( 152×254×2,000 mm ) were constructed and tested. Fatigue flexural failure occurred in 29 of these beams. The study showed that pitting of the steel reinforcement due to corrosion occurred only after about a 7% actual mass loss which coincided with a decrease in the fatigue performance of the beam. The controlling factor for the fatigue strength of the beams is the fatigue strength of the steel bars. Repairing with CFRP sheets increased the fatigue capacity of the beams with corroded steel reinforcement beyond that of the control unrepaired beams with uncorroded steel reinforcement. Beams repaired with CFRP at a medium corrosion level and then further corroded to a high corrosion level before testing had a comparable fatigue performance to those that were repaired and tested after corroding directly to a high corrosion level.

The effect of compressive underloads and tensile overloads on fatigue damage accumulation in SAE 1045 steel

Abstract Block histories containing either compressive underloads or tensile overloads followed by smaller fully reversed cycles were applied to smooth specimens to determine the load interaction effect of large stress cycles on the fatigue behaviour of subsequent smaller cycles. Interactive damage was obtained by subtracting the damage due to the overload and the steady state damage due to the small cycles from unity. As in previous tests on an aluminium alloy, the interactive damage per cycle decays as a power law function of the number of cycles following an underload or overload. The results indicate that small cycles, including those below the constant-amplitude fatigue limit, can contribute significantly to damage accumulation, and therefore small cycles should not be ignored when predicting fatigue lives for variable-amplitude histories.