Assessment of fatigue crack closure under in-phase and out-of-phase thermomechanical fatigue loading using a temperature dependent strip yield model

In this paper fatigue crack closure under in-phase and out-of-phase thermomechanical fatigue (TMF) loading is studied using a temperature dependent strip yield model. It is shown that fatigue crack closure is strongly influenced by the phase relation between mechanical loading and temperature, if the temperature difference goes along with a temperature dependence of the yield stress. In order to demonstrate the effect of the temperature dependent yield stress, the influence of in-phase and out-of-phase TMF loading is studied for a polycrystalline nickel-base superalloy. By using a mechanism based lifetime model, implications for fatigue lives are demonstrated.     

A new expression for crack opening stress determined based on maximum crack opening displacement under tension–compression cyclic loading

The maximum crack opening displacement is introduced to investigate the effect of compressive loads on crack opening stress in tension–compression loading cycles. Based on elastic–plastic finite element analysis of centre cracked finite plate and accounting for the effects of crack geometry size, Young's modulus, yield stress and strain hardening, the explicit expression of crack opening stress versus maximum crack opening displacement is presented. This model considers the effect of compressive loads on crack opening stress and avoids adopting fracture parameters around crack tip. Besides, it could be applied in a wide range of materials and load conditions. Further studies show that experimental results of da/dN ? ΔK curves with negative stress ratios could be condensed to a single curve using this crack opening stress model.     

Fatigue crack growth testing at negative stress ratios: discussion on the comparability of testing results

It is an accepted fact in fatigue community that compressive loads contribute to fatigue crack growth. Evidences range from fatigue crack growth under fully compressive loads to effects of compressive underloads to negative stress ratio loading. Because the crack closes under compression and the crack flanks transmit compressive stresses, the loading situation is completely different to those of tensile loading. The present paper addresses the comparability of crack growth testing procedures at negative stress ratios. It reveals that compressive loading at the crack tip differs in different specimens for an equal maximum stress intensity factor K_max and negative stress ratio R. Furthermore, the crack length can significantly influence the loading conditions at the crack tip for tension–compression loading. Depending on the specimen type and crack length, a negative force ratio may lead to a change of algebraic sign of the stresses at the crack tip or not. As a consequence, the comparability of available literature results for R ≤ 0 tests is not ensured. Proposals to improve the comparability of tension–compression crack growth testing will be given.     

Very high cycle fatigue of VDSiCr spring steel under torsional and axial loading

Very high cycle fatigue (VHCF) properties of VDSiCr spring steel are investigated with ultrasonic equipment under fully reversed cyclic torsion loading and under cyclic axial loading at load ratios R = –1, R = 0.1 and R = 0.5. Shot‐peened specimens with surface finish similar to valve springs in combustion engines are tested until limiting lifetimes of 10¹⁰ cycles. Under cyclic torsion loading, specimens either fail below 10⁶ cycles with crack initiation at the surface or they do not fail. Under cyclic axial loading, failures above 10⁹ cycles were found for all load ratios with crack initiation at the surface or at internal inclusions. Ratio of mean endurance limit (50% failure probability at 10¹⁰ cycles) under fully reversed cyclic torsion and cyclic tension‐compression loading is 0.86. Cyclic torsion loading slightly below the endurance limit leads to cyclic softening first followed by cyclic hardening whereas cyclic stability is found for tension‐compression loading. Cyclic torsion reduces surface compression stresses whereas they are hardly affected by cyclic tension‐compression loading. Mean endurance limit at 10¹⁰ cycles for R = 0.1 is 61% of the endurance stress amplitude at load ratio R = –1, and for R = 0.5 it is 44% of the tension‐compression endurance limit. Endurance limits for cyclic torsion and cyclic tension‐compression loading are comparable, if effective stress amplitude is used that considers cyclic normal stresses and residual compression stresses at the surface.     

Stress intensity factors of a central slant crack with frictional surfaces in plates with biaxial loading

The stress intensity factor is a traditional topic in mechanics and there have been many solutions for many different cases. The closed frictional crack problem has been modeled in the rock mechanics field where fractures are mostly under compression. Further, the effect of finite plate dimensions under biaxial loading has not been considered in the literature. The key contribution of the present paper is to evaluate the effect of the crack length to plate width ratio on the mode I and II stress intensity factors (SIF) of a central slant crack with frictional surfaces in plates with biaxial loading of different patterns, i.e. tension-tension, tension-compression, compression-tension or compression-compression. A plane strain elastic two-dimensional finite element analysis was adopted. Crack length to plate width ratios equal to 0.1, 0.3 and 0.5 with biaxial ratios from –1 to 1, crack angles from 0° to 90° and friction coefficients from 0 to 1 were considered. Contact regimes and the effect of the crack length to plate width ratio were found dependent on biaxial ratio and pattern, friction coefficient and crack angle.     

Fully plastic analyses of plane strain single-edge-cracked specimens subject to combined tension and bending

Accurate yield surfaces of plane strain single-edge-cracked specimens having shallow as well as deep cracks are developed using finite element limit analyses and monotonic interpolation functions. Fully plastic shallow crack configurations are classified based on certain aspects of the yield surfaces. Relationships between incremental plastic crack tip and crack mouth opening displacements and incremental load point displacement/rotation are obtained for a wide range of relative crack depths and loading ratios. Fully plastic crack-tip fields for a sufficiently deep crack in a single-edge cracked specimen are examined to provide the stress triaxiality and the angular orientation of flow line at the crack tip in terms of the remotely applied tension-to-bending ratio. Evidence for fully plastic crack-tip stress fields consisting of an incomplete Prandtl fan and a crack plane constant state region is discussed.     

The influence of compression loads and of dk/da on the crack propagation under variable amplitude loading

During the past 10–15yr the development of crack growth prediction models for variable amplitude loading conditions has reached a high standard. However, there still exist some uncertainties regarding the quantitative effect of compression loads and of the variation of the stress intensity with increasing crack length on the crack propagation.For the evaluation of the influences of compression loads and of $\text{d}\text{K/}\text{d}\text{a}$ simple loading histories with single peak overloads and with compression underloads were run in stress controlled tests as well as in tests where the (reference) stress intensity was kept constant. The test results showed that the influence of $\text{d}\text{K/}\text{d}\text{a}$ was significant for variable amplitude loading conditions, and that this influence has to be considered in realistic crack propagation prediction models.Compression stresses have a strong effect on the crack opening level. Of special importance is the magnitude of the compression load relative to the compression yield strength of a material.A straight forward analytical analysis of the stresses before and behind a propagating crack was performed and a quantitative equation has been derived for the consideration of the influence of compression loads on the crack opening level. The derived equation is compared to the presently availalbe analytical expressions.     

Improved test method for very low fatigue‐crack‐growth‐rate data

Currently, in North America, the threshold crack‐growth regime is experimentally defined by using ASTM Standard E647, which has been shown in many cases to exhibit anomalies due to the load‐reduction (LR) test method. The test method has been shown to induce remote closure, which prematurely slows down crack growth and produces an abnormally high threshold. In this paper, the fatigue‐crack growth rate properties in the threshold and near‐threshold regimes for a titanium alloy, Ti‐6Al‐4V (STOA), are determined by using the LR test method and an improved test method. The improved method uses ‘compression–compression’ precracking, as developed by Pippan, Topper and others, to provide fatigue‐crack‐growth rate data under constant‐amplitude loading in the near‐threshold regime, without load‐history effects. Tests were conducted over a wide range in stress ratios (R = 0.1–0.7) on compact C(T) specimens for three different widths (25, 51 and 76 mm). The slitting method was used on 51 mm C(T) specimens to confirm that the material did not contain significant levels of residual stresses from forming and/or machining. A crack‐mouth‐opening‐displacement gage was used to monitor crack growth. Data from the ASTM LR method gave near‐threshold values that were found to be dependent upon the specimen width. However, data from the compression precracking constant amplitude (CPCA) loading method gave near‐threshold data independent of specimen width. A crack‐closure analysis was performed for both the LR and CPCA data, to correlate data at the various stress ratios. The CPCA data correlated well with the effective stress‐intensity factor range against rate relation, whereas the LR data exhibited significant threshold fanning with both stress ratio and specimen width.     

RATE-DEPENDENT DEFORMATION AND FRACTURE OF α-TITANIUM

Aspects of combined rate-dependent deformation and crack growth in α-titanium at room temperature are examined. Results are presented for tests carried out on pre-cracked three point loaded single edge notch bend and compact tension specimens subjected to constant crack opening displacement rates and constant load. Curves of the ratio of the reference stress to the yield stress as a function of the ratio of the plastic displacement to specimen width are found to be different for different rates. The stress difference between continuously loaded curves and curves obtained from load relaxation tests (“relaxed” curves) is found to be similar to uniaxial results. Earlier uniaxial tests show that the “relaxed” curve represents a boundary below which no further creep takes place. The pre-cracked specimen constant load curves cross the “relaxed” curve, even though the contribution from crack growth to the overall deformation is found to be small. Sustained load crack growth is observed to take place under contained yielding conditions and the sustained load resistance curves are found to be different for different reference stresses.     

High temperature fatigue crack growth in Inconel 718

Abstract

The nickel base superalloys are extensively used in high temperature applications, so it is important to know their behaviour under conditions of high-temperature fatigue. This paper studies the influence of ΔK, loading frequency, stress ratio and temperature on the high temperature fatigue crack growth rate of nickel base superalloys. This study is based on fatigue tests carried out in corner crack specimens of Inconel 718 at 600°C and at room temperature. Three stress ratios (R = 0.05, 0.5 and 0.8) and loading frequencies ranging from 0.0017 to 15 Hz were considered in the tests. For frequencies below 0.25 Hz, the load wave shape was trapezoidal with different dwell times at maximum load. At relatively high frequencies the propagation is cycle dependent, while for lower frequencies it is time dependent. At intermediate frequencies a mixed crack growth occurs. The transition frequencies from cycle dependent to mixed regime and from mixed to time dependent regime were obtained for each R. The increase of R increases the transition frequencies, i.e., extends the time dependent crack growth to higher frequencies. The increase of R also produces an increase of cyclic crack growth rate for all regimes of crack growth. In the time dependent regime, a higher variation is observed, that can be explained by an acceleration of oxidation damage promoted by the increase of maximum stress. An approach for modelling the high-temperature fatigue crack growth in nickel base superalloys is presented. A good agreement was observed between time dependent fatigue results and mathematical models based on static load results.     

Fatigue crack growth for a surface crack in a round bar under multi-axial loading condition

In this paper, the fatigue life, surface crack extension direction and crack growth rate in an elastic bar with a circular cross section are determined through experiments under cyclic torsion with axial static and cyclic tension/compression loading. The effects of the loading type, loading value and stress ratio on the crack growth behaviour are discussed. The results show that, under pure fatigue torsion loading, the crack extension direction is almost the same whatever the value of torsion loading. Under fatigue torsion with cyclic tension loading, it is found that the crack extension direction is mainly determined by the alternating parts of the stresses and is almost independent of the average parts of the stresses, whereas the fatigue life is obviously dependent on the average stress.     

Determination of the opening load for a growing fatigue crack: evaluation of experimental data reduction techniques and analytical models

In metallic materials, growing cracks will remain closed or partially closed for a portion of the applied cyclic load as a consequence of plastically deformed material left in the wake of a growing crack, surface roughness along the crack surfaces, or corrosion debris. Proper characterization of this crack closure and the subsequent opening load is required for accurate prediction of crack growth. In the laboratory, global load–displacement data are commonly used in conjunction with a data reduction technique to estimate the opening load for a growing crack. Different data reduction techniques will be compared, and the influence of data smoothing will be demonstrated, using AA 7075-T651 specimens tested under constant amplitude cyclic loading with load ratios R = 0.1, 0.2, and 0.3. The ratio of maximum stress intensity factor to plane strain fracture toughness was approximately K _max / K _Ic = 0.5. The measured crack opening loads are also compared with predictions obtained from two different strip-yield models and three-dimensional elastic–plastic finite element analyses. Results show the necessity of using smoothed data, and the poor behaviour of the compliance offset data reduction technique, when analysing high load ratio data. A modification to this technique is proposed which improves crack opening load estimates. Overall, the analytical model predictions compare well with the experimental results; especially those results generated using the modified compliance offset technique.     

Fatigue of 7075-T651 aluminum alloy under constant and variable amplitude loadings

The fatigue crack growth (FCG) behavior of 7075-T651 aluminum alloy was studied under constant and variable amplitude loadings in vacuum, air and 1% NaCl solution. In the study of constant amplitude loading fatigue, the stress ratios were 0.1 and 0.85 and the loading frequency was 10 Hz. In the study of variable amplitude loading fatigue, the load spectrums were tension type and tension–compression type, and the average loading frequency was about 5 Hz. The results of FCG tests, under constant and variable amplitude loadings, validated the unified two parameter driving force model, accounting for the residual stress and stress ratio effects on fatigue crack growth.     

Fatigue crack growth in 7249‐T76511 aluminium alloy under constant‐amplitude and spectrum loading

Fatigue crack growth tests were conducted on compact, C(T), specimens made of 7249‐T76511 aluminium alloy. These tests were conducted to generate crack growth rate data from threshold to near fracture over a wide range of load ratios (R). Four methods were used to generate near threshold data: (1) ASTM E‐647 load reduction (LR), (2) compression pre‐cracking constant‐amplitude (CPCA), (3) compression pre‐cracking LR, and (4) constant crack mouth opening displacement LR method. A crack closure analysis was used to develop an effective stress‐intensity factor range against rate relation using a constraint factor (α = 1.85). Simulated aircraft wing spectrum tests were conducted on middle crack tension, M(T), specimens using a modified full‐scale fatigue test spectrum. The tests were used to develop the constraint‐loss regime (plane strain to plane stress; α = 1.85 to 1.15) behaviour. Comparisons were made between the spectrum tests and calculations made with the FASTRAN life prediction code; and the calculated crack growth lives were generally with ±10% of the test results.     

Plastic strain distribution at the tip of a fatigue crack. application to fatigue crack closure in the threshold regime

The fatigue crack growth rate behaviour of a Co-33 wt pct Ni alloy was investigated at room temperature down to the threshold regime using CT specimens for two load ratios 0.1 and 0.3. Cyclic equivalent plastic strain distributions along an axis normal to the crack plane were experimentally determined over the whole range of crack growth rates using two techniques microhardness and a quantitative metallographic technique applied to twins, both calibrated on low cycle fatigue specimens. These experimental values were compared with theoretical curves as obtained from the monotonic plane strain finite element analysis of Tracey and adapted to cyclic loading according to the procedure proposed by Rice. A good agreement was found in stage II crack growth in the vicinity of the crack tip but a discrepancy was observed in the low crack growth rate regime, indicative of crack closure. It was possible to determine the effective amplitude of the stress intensity factor which accounts for this discrepancy and an intrinsic crack growth law was obtained which obeys Paris equation and which applies in the whole crack growth rate range independently of the load ratio.     

A unified fatigue failure criterion for unidirectional laminates

A unified fatigue failure criterion using micromechanics related to the fracture plane has been developed to predict fatigue lives of unidirectional fibre reinforced polymer composites subjected to cyclic off-axis tension–tension loading. Since the failure criterion incorporates both stresses and strains it may be characterized as energy based. Accounting for the fibre load angle as well as the stress ratio is the novelty of this fatigue failure criterion. The criterion only requires the stress ratio to be known from the experimental procedure. The relation between the applied load and the micro-stress and micro-strain field can be determined from a numerical method. The fatigue failure criterion has been verified by applying it to different sets of experimental data. Several fibre load angles, different fibre/matrix combinations as well as stress ratios are covered. The predicted fatigue lives are in good agreement with the experimental results for both different fibre load angles and stress ratios.     

Unified triaxiality at the crack tip subjected to plane strain condition under mixed‐mode (I + II) fracture

The new model of stress triaxiality, subjected to plane strain condition under mixed‐mode (I + II) loading, at the yield loci of the crack tip, has been formulated using unified strength theory. It evaluates critical values of triaxiality for various convex and non‐convex failure criteria, unlike the existing model. It shows the effects of Poisson's ratio and intermediate principal stress for materials whose strength in tension and compression is either equal or unequal. Further, on this basis, the crack initiation angles are predicted for various crack inclinations and compared with those obtained from other fracture criteria. The plastic zone shapes supplement the results. Critical yield stress factor, a significant parameter at the crack tip got lowered as the difference among the three principal stresses reduced to a minimum. The crack initiation angles obtained from the model showed good agreement with those obtained from G‐, S‐, and T‐criterion.     

Numerical prediction of creep crack growth in different geometries using simplified multiaxial void growth model

Abstract

This paper considers the prediction of creep crack growth (CCG) in different fracture mechanics geometries using finite element (FE) analysis based on a material independent simplified multiaxial failure strain model at the crack tip. The comparison is first made by modelling C(T) specimen tests under plane stress and plane strain conditions using creep properties of a C–Mn steel at 360°C. In addition, in order to examine CCG due to different geometries, a single edge notch specimen (SENT), centre cracked tension specimen (CCT) and three-point bending (3PB) specimen have been modelled and analysed. In all cases, it is found, depending on the geometry, that for this steel at low creep temperatures the applied load develops a high reference stress/yield stress (σ_ref/σ_y) ratio, which helps reduce constraint at the crack tip. The predictions are analysed under plane stress/plane strain loading conditions identifying the effects of geometry on cracking rates and the implications for predicting long term test or component failure times exceeding where the applied σ_ref/σ_y<<1.     

The evolution of the stress–strain fields near a fatigue crack tip and plasticity-induced crack closure revisited

The evolution of the stress–strain fields near a stationary crack tip under cyclic loading at selected R‐ratios has been studied in a detailed elastic–plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R‐ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic–plastic finite element simulations of advancing fatigue cracks were carried out under plane‐stress, plane‐strain and generalized plane‐strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane‐strain and generalized plane‐strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane‐stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack‐closure measurement, and indeed on the role of plasticity‐induced crack closure in the reduction of the applied stress intensity factor range.     

Some comments on the effect of biaxial stress on fatigue crack growth and fracture

The influence of biaxial loading on plastic zone size and crack opening displacement has been examined. Loading parallel to the crack plane was accounted for in satisfying the yield criteria, proposed by Von Mises, along the crack plane. Comparing plastic zone sizes for biaxial and uniaxial loading, when the applied stress normal to the crack plane is the same in both cases, shows a reduction of up to 65 per cent in plastic zone size for the biaxial loading case. The crack opening displacement is also reduced up to 33 per cent for biaxial loading. Based on critical crack opening displacement, fatigue crack propagation rates would be lower than for uniaxial loading, and an apparent increase in fracture toughness would also occur. The theoretical predictions are supported by a limited amount of experimental data.