Range Of Stress Ratios Research Articles

TRANSIENT FATIGUE CRACK GROWTH BEHAVIOUR FOLLOWING SINGLE OVERLOADS AT HIGH STRESS RATIOS

Abstract—Fatigue crack growth tests with constant amplitude loading and single overload have been performed on a long mode I crack in 2017‐T3 aluminium alloy at various stress ratios from 0 to 0.7. Two crack tip parameters of σop and σtt were evaluated using a finite element analysis for a growing crack under these loading conditions. The former is the crack opening stress and the latter is the applied stress level at which the stress at the crack tip becomes tensile. It was found that transient crack growth behaviour following single overloads at high stress ratios was significantly different from that at a low stress ratio: at higher stress ratios, following the application of the overload, there was a rapid retardation which was followed by an acceleration in growth rate and then a faster return to the steady state level at baseline loading. The experimentally observed transient post‐overload behaviour is discussed in terms of the two effective stress range ratios of Uop and Utt, which are determined from σop and σtt, respectively. For the stress ratios and overload ratios studied, the results indicate that the changes in Utt with crack extension after the overload are reasonably consistent with the crack growth rate trends. The stress distribution at minimum applied stress would account for the transient changes in Utt.

Study of fatigue crack characteristics by acoustic emission

Acoustic emission (AE) technique was used to investigate fatigue crack characteristics such as initiation closure and propagation on smooth specimens of Incoloy 901 at room temperature, over the range of stress ratios −1.0 ⩽ R ⩽ 0.2. AE technique was applied to determine when and where a microcrack initiated on the specimens. The threshold stress intensity ranges were determined by combining AE tests and microscopic examination for crack initiation points. The AE technique revealed the crack closure process in smooth specimens, and crack-opening/closing stress was easily determined from the AE signature. Several published formulae for crack-opening stress were examined. During crack propagation, AE count rate and total counts, associated with the crack growth state, were stress- and lifetime-dependent. The results showed a nonlinear relation between the AE count rate and the crack propagation rate.

FATIGUE CRACK GROWTH AND CLOSURE AT HIGH STRESS RATIOS

Abstract— Fatigue crack growth tests have been carried out on a medium carbon structural steel over a wide range of stress ratios, i.e. from 0 to 0.7. All tests were conducted under constant amplitude loading conditions corresponding to growth rates in the Paris regime. Crack closure behaviour was observed experimentally by a surface strain gauge technique, and numerically by a finite element analysis under plane stress condition. While the crack closure could not be detected by experimental measurements at stress ratios equal to or greater than 0.5, the numerical results showed that closure occurred even at high stress ratios up to 0.7. The differences between experimentally and numerically determined crack opening levels were found for each stress ratio. A cause for these differences is discussed. In addition, two new types of crack tip parameters which have been proposed recently are evaluated by finite element analysis and their relevance to fatigue crack growth are discussed. It is concluded that fatigue crack growth rates are substantially determined by the effective stress intensity factor range which is based on the crack closure concept.

Fatigue Design Model Based on Damage Mechanisms Revealed by Acoustic Emission Measurements

Integration of the microcomputer into acoustic emission instrumentation has brought AE monitoring of fatigue tests into the realm of practicality. On-line processing makes available a selection of software tools, enhancing classical techniques for eliminating the background noise which usually blanked out the desired data. Fatigue tests monitored for acoustic emission were carried out at room temperature on Incoloy 901 material specimens, over a stress-ratio range of −1 ≤ R ≤ .2. Valid AE data were obtained even when the load cycle passed through zero. The AE data permitted specific identification of the various phenomena occurring on the way to final failure. These included initial plasticity, crack nucleation and propagation phases. The AE findings were supported by microscopic examination. Based on the experimental data, a preliminary damage-prediction model was formulated.

A theory for initial yield conditions in tube bulging with a urethane rod

Making use of experimentally determined friction-characteristics of urethane under pressure, the initial yield conditions in tube bulging with an internal urethane rod are analyzed. The analysis predicts a neutral cross-section where the urethane friction changes direction. The effects of the tube diameter, the length of the urethane rod, the applied pressure and the material properties on the position of the neutral zone are determined and the effects of various process parameters on the range of stress ratios that exist at initial yield of the tube being bulged are studied, the initial yield conditions predicted by the present analysis being compared with those from an earlier analysis.

Measurement of the effects of stress ratio and changes of stress ratio on fatigue crack growth rate in a quenched and tempered steel

This paper describes a technique that enables fatigue crack growth rate to be determined for a range of stress ratios, R, using a single specimen. The procedure eliminates some of the scatter normally encountered when data are obtained from multiple specimens. In the process of verifying the procedure, the effect of R on the fatigue crack growth rate in steel Q1N, and the effect of increases and decreases in R, have been examined. Change in the stress ratio causes significant change in the crack growth rate in the Paris regime, but transient effects are not observed unless the maximum stress intensity factor at the crack tip is reduced by more than about 10%.

Cyclic response and substructure evolution of copper polycrystals: Llanes, L.M. Diss. Abstr. Int. (Jan. 1993) 53 (7)

In previous work, fatigue-crack-growth tests were conducted on middle-crack tension, M(T), and compact, C(T), specimens made from the same D16Cz (clad) aluminum alloy sheet. These tests were conducted over a wide range of stress ratios (R = Pmin/Pmax = −0.5 to 0.75) to generate crack-growth-rate data from threshold to near fracture. These tests were used to generate the effective stress-intensity factor range (ΔKeff) against rate curve using a crack-closure model. The analyses collapsed the rate data from both specimen types into a fairly narrow band over many orders of magnitude in rates using proper constraint factors. Constraint factors were established from single-spike overload and the constant-amplitude tests. Herein, the life-prediction code, FASTRAN, which is based on the strip-yield model concept, was used to calculate the crack-length-against-cycles under constant-amplitude (CA) loading and the single-spike overload (OL) tests; and to predict crack growth under variable-amplitude (VA) loading and simulated aircraft loading spectrum tests on the M(T) specimens. The calculated crack-growth lives under CA and an OL tests were generally within ±20% of the test results, but slower crack growth under the double-shear fatigue mode, rather than single shear, may be the reason for some of the larger differences. The predicted crack-growth lives for the VA and Mini-Falstaff spectrum tests were also short by 25–45%. A modified model with some assumed notch constraint effects matched the spectrum tests quite well. Issues on the crack-starter-notch effects under spectrum loading are discussed, and recommendations are suggested on avoiding these notch effects.

Morphological Aspects of Fatigue Crack Growth under Biaxial Loading Conditions

In order to investigate the fatigue crack growth behavior under various biaxial loading conditions, twelve pieces of welded fatigue test specimen are designed in such a manner that the repeated nominal biaxial stress range ratios vary from 0.2 to 2.0 at the orthogonal joint of the specimen. It is of great interest to understand the sharp crack turning under certain biaxial loading conditions, where a crack changes its propagating direction approximately perpendicular to the initial direction. Various morphological modes of fatigue failure are actually obtained by experiments in the present work.It is also important to estimate an accurate crack path by numerical simulation for the proper understandings of fatigue crack propagation behavior. A step-by-step finite element approach has been proposed for fatigue crack path prediction, in which a two-dimensional cracked domain is remeshed by the modified quadtree mesh generation algorithm, and the stress field ahead of the current crack tip is analyzed by taking account of the higher order stress field parameters. A curved crack increment can be determined by using the first order perturbation solution together with the local symmetry criterion. The crack tip extends for a certain increment size, and the procedure is repeated for the next step. The present method is applied to the simulations of the fatigue test specimens. It is found that the simulated crack paths are in fairly good agreement with the experimental results and that the curved paths of fatigue cracks could be greatly influenced by the biaxial stress ratios, the loadings, and the geometry of the stress concentration corner.Although fairly good agreements are obtained between the simulated crack growth lives and the experimentally obtained ones for simple three point bending specimens in a previous paper, significant discrepancies are sometimes observed in the present study. We have not had the definite answer to the question, but one of the sources of the disagreement could be the compressive welding residual stress in the test specimens, which could significantly reduce the effective stress intensity ranges of some specimens.

Some formulae for the effective stress range ratio used in crack growth of 6063-T6 aluminium alloy

The influence of stress ratio R and stress intensity range ( ΔK) on fatigue crack growth experiments were determined for 6063-T6 aluminium alloy and crack growth data were analysed with different formulae for the effective stress intensity range ratio U. The data covered R values from 0 to 0·3. A good correlation was obtained from da dN and ΔK eff using the equation for U as a function of R.

Creating an in-house shot peening specification for gears. I: Lawerenz, M. and Ekis, I. Heat Treating24 2 (Feb 1992) pp 22–29

The fatigue behaviour of a unidirectional composite lamina is examined from theoretical and experimental viewpoints. The goal is to establish a technique to use experimental data from a unidirectional ply under uniaxial fatigue to simulate the behaviour of that ply in multiaxial fatigue loading. Traditional polynomial failure criteria for fatigue are of limited use because fatigue strength is a function of number of cycles and applied fatigue stress ratio. In practice, a problem such as a fatigue-loaded complex composite structure containing stress concentrations, is subjected to varying stress ratios at different points, especially if material or geometric nonlinearities are involved. However, fatigue testing under a wide range of stress ratios is time consuming and expensive. Therefore it is important to establish a technique to consider fatigue damage due to arbitrary stress ratio without having to perform excessive amounts of testing. Here the theoretical basis of a new model, called the generalized residual material property degradation model is explained in detail.

The influence of environment on fatigue crack growth of an Fe3Al, Cr alloy: Castagna, A. and Stoloff, N.S. Scr. Metall. Mater. Feb. 1992 26, (4), 673–678

This paper summarizes some of the fatigue-crack-growth-rate data generated in the threshold and near-threshold regimes on two aluminum alloys (7075-T651, 7075-T7351), a titanium alloy (Ti–6Al–4V β-STOA), a high-strength 4340 steel and a nickel-based superalloy (Inconel-718) using compression precracking constant-amplitude (CPCA), compression precracking load-reduction (CPLR), and the ASTM E-647 load-reduction (LR) test methods. Tests were conducted over a range in stress ratios (R = 0.1, 0.4 and 0.7) on compact specimens. One of the aluminum alloys (T651) and the 4340 steel showed very little difference between the methods; however, the other three materials showed significant differences with the compression precracking test methods giving lower thresholds and faster crack-growth rates than the load-reduction test method. Materials that have shown significant differences exhibited either rough crack-surface profiles (7075-T7351, Ti–6Al–4V β-STOA) or produced fretting debris along the crack surfaces in the threshold and near-threshold regimes (Inconel-718).

A Computational Approach for the Prediction of Fatigue Crack Growth along Non-collinear Paths

Proper understandings of fatigue crack propagation behavior with adequate accuracy are extremely important for the evaluation of ship structural strength and performance, where the prediction of a crack path is prerequisite. A step-by -step finite element approach has been proposed for fatigue crack path prediction, in which a cracked domain is remeshed by an automatic mesh generation algorithm and the stress field ahead of the current crack tip is analyzed by applying the method of superposition of analytical and finite-element solutions. Using the stress field parameters ahead of the crack tip, a curved crack increment can be determined by the first order perturbation solution together with the local symmetry criterion. The crack tip then extends for a certain increment size and the procedure is repeated for next steps.Since the modified quadtree algorithm previously implemented has some difficulties in dealing with geometric boundary, several improvements in the computational code have been made in this research so that the possibility of erroneous meshing on boundary line, boundary corner and crack line is significantly reduced. A circular region around a crack tip with a prescribed regular mesh pattern is introduced, and an integer coordinate system, which naturally fits for the global geometry of the domain, is chosen so that quadrilateral elements with nearly square shape almost cover the whole domain except in the vicinity of curved boundaries.Simple non-collinear fatigue crack propagation experiments are carried out. The stress intensity factors along measured crack paths are evaluated and the validity of the local symmetry criterion, on which the crack path prediction of this approach is based, is examined. It seems that the criterion is not regorously satisfied, but can be used as an approximate condition. Based on numerical data from computational experience a proper selection of an increment size in each step is discussed. It is observed that, for example, if KII/KI is kept below 2-3 % for a reasonable crack path prediction, the increment size should be chosen to be less than 20-25 % of the minimun distance from the current crack tip to the boundary.Once a fatigue crack is initiated in a welded structure, its propagation path is believed to be governed by a macroscopic stress distribution. Particularly in the case of biaxial stress distribution, it is possible that the initial crack propagation direction could be much changed as it extends for some distance. In this research the propagation behavior of a crack at a stress concentrated corner of a cruciform specimen is studied. Numerical crack path predictions are carried out for various external loading conditions (biaxial tension, biaxial in-plane bending, tension-bending), with various biaxial stress range ratios.

Crack Closure and Propagation Studies to Determine the Effects of Simple Load Interaction

Crack closure and fatigue crack growth experiments were performed on centrally notched specimens of 6063-T6 Al-alloy under single overload and block loading conditions. Using crack closure data, values of effective stress range ratio (U) were found. Assuming that the crack closure phenomenon is responsible for transient behavior of fatigue crack growth rate (FCGR), the FCGR behavior during load interaction was predicted using a constant amplitude crack propagation description in conjunction with the experimentally measured U-values. On comparing predicted FCGR with those found experimentally, it was observed that the predicted FCGR always agrees with the trend of experimental FCGR behavior and provides either exact or conservative estimates of the FCGR.

A Simple Model for Fatigue Crack Growth Near Stress Concentrations

Fatigue crack growth rates are often difficult to predict for short cracks growing near stress concentrations. This paper presents a simple model to predict those growth rates which incorporates the phenomenon of crack closure. Crack opening stresses are shown to change significantly as cracks grow away from notches, and the simple model is designed to describe those changes. The effective stress range ratio, U, is assumed to be dependent on the local stress at the crack tip location in a corresponding uncracked body. The value of U changes with the normalized maximum stress in unnotched bodies, and this dependence can be quantified with elastic-plastic finite element models or simpler modified-Dugdale crack analyses. The local stress distribution is estimated with a Neuber analysis. A semi-empirical stress intensity factor solution is constructed and calibrated with known exact solutions. The crack growth rate is then calculated with the modified Paris law, taking crack growth constants from long crack data. The model is illustrated with a specific case study, the growth of cracks from center notches in an SAE 1026 steel. Experimental crack growth data for notches of different sizes and shapes compare favorably with the calculations. The scheme is contrasted with previous models for notch fatigue cracks. The implications of the simple model for other fatigue design problems are explored, highlighting the simplicity and generality of the model.

Considerations of grain orientation and work hardening on short-fatigue-crack modelling: de los Rios, E.R. and Navarro, A. Philos. Mag. A Mar. 1990 61, (3), 435–449

Centrally cracked specimens of JIS SM58Q and HT80 steels were fatigued. The fatigue crack growth rates, da/dn, and the stress intensity threshold levels, ΔKth were measured over the range of stress ratio, R, from −1 to 0.8 by the use of an automatic method of continuously decreasing stress intensity factor with crack extension. The measured ΔKth was well represented as |ΔKth/2|R=(1−R)γ|ΔKth/2|R=0; and the propagation rate, as da/dn = A(1−R)γm[(ΔK/2)m − {(1 − R)γ|ΔKth/2|R=0}m] for −1≦R≦0.33 or da/dn = A(1 − 0.33)−γm [(ΔK/2)m {(1 − R)γ |ΔKth/2|R=0}m] for 0.33 < ≦ 0.8.

Evaluation of actual fatigue stress by using striation spacing and hardness: Ishida, S., Tokumasu, M., Nakasa, K. and Ishihara, H. J. Soc. Mater. Sci., Japan Jan. 1990 39, (436), 63–69 (in Japanese)

Centrally cracked specimens of JIS SM58Q and HT80 steels were fatigued. The fatigue crack growth rates, da/dn, and the stress intensity threshold levels, ΔKth were measured over the range of stress ratio, R, from −1 to 0.8 by the use of an automatic method of continuously decreasing stress intensity factor with crack extension. The measured ΔKth was well represented as |ΔKth/2|R=(1−R)γ|ΔKth/2|R=0; and the propagation rate, as da/dn = A(1−R)γm[(ΔK/2)m − {(1 − R)γ|ΔKth/2|R=0}m] for −1≦R≦0.33 or da/dn = A(1 − 0.33)−γm [(ΔK/2)m {(1 − R)γ |ΔKth/2|R=0}m] for 0.33 < ≦ 0.8.

Photoelastic analysis of friction-grip bolted joints: Czerkas, K., Kratena, J., Bartos, F., Junkova, S. and Kratenova, M. Acta Tech. CSAV 1990 35, (1), 93–102

Fatigue-crack-growth tests were conducted on compact, C(T), specimens made of D16Cz (clad) aluminum alloy under constant-amplitude loading, a single spike overload, and simulated aircraft spectrum loading. Constant-amplitude tests were conducted to generate crack-growth-rate data from threshold to near fracture over a wide range of stress ratios (R = Pmin/Pmax = 0.1–0.75) using the new compression pre-cracking test methods. Comparisons were made between test data generated on the C(T) specimens with test data from the literature on middle-crack-tension, M(T), specimens machined from the same sheet. A crack-closure analysis was used to collapse the rate data from both specimen types into a narrow band over many orders of magnitude in rates using proper constraint factors. The constraint factors were established from constant-amplitude (CA) and single-spike overload tests. The life-prediction code, FASTRAN, which is based on the strip-yield model concept, was used to calculate crack-length-against-cycles under CA loading and a single-spike overload (OL) test, and to predict crack growth under simulated aircraft spectrum loading tests on C(T) specimens. The calculated crack-growth lives under CA loading were generally within about ±25% of the test results, but slower crack growth under the double-shear fatigue mode, unlike the single-shear mode (45o slant crack growth), may be the reason for some of the larger differences. The predicted results under the single-spike overload and the Mini-Falstaff+ spectrum were within 10% of the test data.

Effect of oxidation on high-temperature, high-cycle fatigue behaviour of engineering steels: Kanazawa, K., Sato, M. and Kimura, M. J. Soc. Mater. Sci., Japan Feb. 1990 39, (437), 175–180 (in Japanese)

Fatigue-crack-growth tests were conducted on compact, C(T), specimens made of D16Cz (clad) aluminum alloy under constant-amplitude loading, a single spike overload, and simulated aircraft spectrum loading. Constant-amplitude tests were conducted to generate crack-growth-rate data from threshold to near fracture over a wide range of stress ratios (R = Pmin/Pmax = 0.1–0.75) using the new compression pre-cracking test methods. Comparisons were made between test data generated on the C(T) specimens with test data from the literature on middle-crack-tension, M(T), specimens machined from the same sheet. A crack-closure analysis was used to collapse the rate data from both specimen types into a narrow band over many orders of magnitude in rates using proper constraint factors. The constraint factors were established from constant-amplitude (CA) and single-spike overload tests. The life-prediction code, FASTRAN, which is based on the strip-yield model concept, was used to calculate crack-length-against-cycles under CA loading and a single-spike overload (OL) test, and to predict crack growth under simulated aircraft spectrum loading tests on C(T) specimens. The calculated crack-growth lives under CA loading were generally within about ±25% of the test results, but slower crack growth under the double-shear fatigue mode, unlike the single-shear mode (45o slant crack growth), may be the reason for some of the larger differences. The predicted results under the single-spike overload and the Mini-Falstaff+ spectrum were within 10% of the test data.

Reliability of soldered joints: a description of the state-of-the-art: de Kluizenaar, E.E. Solder. Surf. Mt. Technol. Feb. 1990 (4), 27–38

In previous work, fatigue-crack-growth tests were conducted on middle-crack tension, M(T), and compact, C(T), specimens made from the same D16Cz (clad) aluminum alloy sheet. These tests were conducted over a wide range of stress ratios (R = Pmin/Pmax = −0.5 to 0.75) to generate crack-growth-rate data from threshold to near fracture. These tests were used to generate the effective stress-intensity factor range (ΔKeff) against rate curve using a crack-closure model. The analyses collapsed the rate data from both specimen types into a fairly narrow band over many orders of magnitude in rates using proper constraint factors. Constraint factors were established from single-spike overload and the constant-amplitude tests. Herein, the life-prediction code, FASTRAN, which is based on the strip-yield model concept, was used to calculate the crack-length-against-cycles under constant-amplitude (CA) loading and the single-spike overload (OL) tests; and to predict crack growth under variable-amplitude (VA) loading and simulated aircraft loading spectrum tests on the M(T) specimens. The calculated crack-growth lives under CA and an OL tests were generally within ±20% of the test results, but slower crack growth under the double-shear fatigue mode, rather than single shear, may be the reason for some of the larger differences. The predicted crack-growth lives for the VA and Mini-Falstaff spectrum tests were also short by 25–45%. A modified model with some assumed notch constraint effects matched the spectrum tests quite well. Issues on the crack-starter-notch effects under spectrum loading are discussed, and recommendations are suggested on avoiding these notch effects.

Orientation of hydraulic fractures in salt under hydrostatic and non-hydrostatic stresses

Laboratory experiments of hydraulic fracturing in salt have shown that the breakdown pressure does not vary significantly with the differences between the maximum and minimum stresses normal to the borehole axis. The presence of a non-hydrostatic stress in salt may be determinable from the form of the hydraulic fracture alone. A series of laboratory experiments were performed to determine the influence of deviatoric in situ stress on the form and orientation of hydraulic fractures in salt. The hydraulic-fracturing tests were run on prismatic blocks in a polyaxial loading frame over a range of stress ratios from 1 (hydrostatic) to 1.5. The fracturing oil contained a fluorescent dye that marked the fracture traces for mapping after the samples were split. The results indicate that the form of the hydraulic fracture reflects whether or not the stresses are nearly hydrostatic. For large stress ratios ( >1.5), the fractures are straight and strongly oriented. For stress ratios near one, the fractures are poorly oriented and exhibit significant branching. Thus, proximity to hydrostatic conditions can be determined from the form of the hydraulic fracture alone, regardless of ambiguities in the interpretation of pressure-time records from the fracturing experiment.