Improvement of ASTM compliance offset method for precise determination of crack opening load

There are two serious drawbacks to the ASTM offset method for determination of crack opening load, discontinuity and inconsistency problems. The former is the lack of opening load value in the lower 5% load range due to the procedure that the compliance offset is plotted against the mean load of the segment span of 10% of the cyclic load range. The latter is that the ASTM method underestimates, estimates accurately, or overestimates the opening load, depending on the maximum compliance offset value and the stress ratio. To overcome the two drawbacks, the so-called normalized-extended ASTM method is proposed and evaluated quantitatively in detail using the data of 7475-T7351 and 2024-T351 aluminum alloys. The normalized-extended ASTM method improves the standard ASTM method significantly and provides very good correlation of crack growth rate stress ratio effects. The normalized-extended ASTM method is strongly recommended for crack opening load determination.     

疲劳裂纹扩展中裂纹尖端应变变化的详细考察

传统的ASTM2%偏差法和卸载弹性法是以柔度轨迹的线性区段确定开闭口载荷(Pop和Pcl),往往因人工误差导致结果相差很大.本文注重裂纹尖端塑性变形带给柔度变化的物理意义,描述了一个载荷循环下柔度变化与裂纹开闭口以及弹塑性行为的关系.采用自行开发的高精度局部柔度测量法,针对结构钢进行了疲劳试验,记录了裂纹尖端应变与载荷关系的系列迟滞回线,并以微分法定量求出迟滞回线上的特征载荷.根据试验考察结果,分析了文献中几种疲劳裂纹扩展参量的关系.结果表明,ΔKRPG比ΔKcl和ΔKop更适合作为裂纹扩展驱动力参量.     

AN EXPERIMENTAL STUDY ON THE OPENING AND CLOSURE BEHAVIOUR OF FATIGUE SURFACE, CORNER AND THROUGH-THICKNESS CRACKS AT NOTCHES

Abstract— The opening and closure behaviour of surface, corner and through-thickness cracks in thin notched plates of FeE460 ( K _t= 2.5) and A15086 ( K _t= 3.4) was experimentally studied. The cracks were initiated and examined under uniaxial fully reversed constant amplitude and two-step loading. Crack opening load values were measured during crack growth in notch sections with a nonuniform stress distribution using small strain gauges glued to the specimen surface, very close to the crack tip. The results represent a comprehensive set of experimental data for crack opening load values in dependence on crack lengths a, c and load level including the influence of overloads and covering all types of cracks. The results indicate uniform relationships between crack opening load levels and all crack types. Crack opening and closure occur at nearly the same strain level, which depends on the applied load level. The crack opening load values measured at large notched specimens differ from those measured at similar smaller specimens because of the different local stress gradients.     

Fatigue crack growth and crack closure in an AlMgSi alloy

This study reports an experimental investigation of fatigue crack propagation in AlMgSi1-T6 aluminium alloy using both constant and variable load amplitudes. Crack closure was monitored in all tests by the compliance technique using a pin microgauge. For the constant amplitude tests four different stress ratios were analysed. The crack closure parameter U was calculated and related with Δ K and the stress ratio, R . The threshold of the stress intensity factor range, Δ K _th , was also obtained. Fatigue crack propagation tests with single tensile peak overloads have been performed at constant load amplitude conditions. The observed transient post overload behaviour is discussed in terms of the overload ratio, Δ K baseline level and R . The crack closure parameter U trends are compared with the crack growth transients. Experimental support is given for the hypothesis that crack closure is the main factor determining the transient crack growth behaviour following overloads on AlMgSi1-T6 alloy for plane stress conditions.     

FATIGUE CRACK GROWTH OF SILICON NITRIDE WITH CRACK WEDGING BY FINE FRAGMENTS

Abstract— Fatigue crack growth tests of silicon nitride Si₃N₄ were carried out under four-point bending using square bar specimens at room temperature. A pre-crack was introduced by a bridge indentation method. Decreasing K -type tests at stress ratios of R = 0.1 and 0.6 and also under static load were first carried out, and after observing the cessation of crack growth, K -increasing tests were performed except for the case of a static load. Crack closure was observed on most specimens by the elastic compliance method. Furthermore, SEM observations of the crack paths were made to see what was happening during crack growth. The threshold and the region of steady crack growth were observed more clearly under cyclic loading, and an effect of load cycling certainly existed which became more evident when the maximum stress intensity factor K _max approached the threshold. A wedge effect, caused by fine fragments on the crack surface, played an important role in crack closure behaviour of each specimen, and it is suggested that the crack growth rate is controlled by both the effective stress intensity range Δ K _eff and the effective mean stress intensity factor K _m,eff at least as a first approximation.     

Fatigue properties of ultrafine grained low carbon steel produced by equal channel angular pressing

Ultrafine grained low carbon (0.15 wt.% C) steel produced by equal channel angular pressing (ECAP) was tested for investigating fatigue properties, including cyclic softening and crack growth rate. Emphasis was placed on investigating the effect of load ratio on the fatigue crack growth rates of ultrafine grained microstructure. The ECAPed steel exhibited cyclic softening. After the first cycle, the tension and compression peak stresses decreased gradually with the number of cycles. Fatigue crack growth resistance and the threshold of ECAPed ultrafine grained steel were lower than that of an as-received coarse grained steel. This was attributed to a less tortuous crack path. The ECAPed steel exhibited slightly higher crack growth rates and a lower ΔK_th with an increase in R ratio. The R ratio effect on growth rates and ΔK_th was basically indistinguishable at a lower load ratio (R>0.3) compared with other alloys, indicating that the contribution of the crack closure vanished. This was explained by the fact that finer grained materials produce a lower opening load P_op due to a relatively less serrated crack path. Consequently, K_min can reach K_op readily with a smaller increment of load ratio. The crack growth rate curve for the ECAPed ultrafine grained steel exhibited a linear extension to the lower growth rate regime than that for the coarse grained as-received steel. This behavior can be explained by a reverse crack tip plastic zone size (r_p) that is always larger than the grain size.     

AN APPROACH TO MEASURE THE SHAPES OF THREE-DIMENSIONAL SURFACE CRACKS DURING FATIGUE CRACK GROWTH

This study presents a technique for measuring shapes of three dimensional surface cracks continuously during fatigue crack growth. The technique uses a laser interferometric system to measure crack compliance and a photomicroscopic system to measure surface crack length. Using a compliance expression for surface cracks, valid for the range of crack aspect ratios (a/c) of 0.2 to 2.0, aspect ratio calculations employing compliance and surface crack length measurements are demonstrated for cracks growing from EDM notches of different geometries (shallow or deep). The experimentally determined aspect ratio variations during cyclic crack growth are shown to be in good agreement with the expected variations in aspect ratio, predicted using the stress intensity factor equations for surface cracks. The effects of deviations in the compliance measurement location from the center of the surface crack due to assymetric crack growth are also accounted for through corrections of compliance measurements for crack-asymmetry. The fatigue crack growth rates of surface cracks, after incorporating the variations in aspect ratio in the calculations, agreed with the large-crack growth data for all crack geometries.     

A microcomputer control system for the measurement of fatigue crack growth data

A microcomputer-based system for the measurement of fatigue crack growth da/dn versus cyclic stress intensity factor ΔK data using compact-tension test specimens is described. The procedure has been developed to allow automatic measurement of crack growth rate under any specified combination and sequence of load conditions, i.e. ΔK and R (stress ratio) and includes the capability of establishing the threshold cyclic stress intensity factor ΔK₀. Crack extension measurement is effected from the elastic compliance evaluated from the AC component of the load and displacement signals to an accuracy of -3 μm every 1000 load cycles. Results from a typical low-alloy-steel rotor forging are presented to illustrate the use of the system.     

NON-ISOTHERMAL FATIGUE CRACK GROWTH IN HASTELLOY-X

Abstract— Non-isothermal fatigue crack growth tests were performed on Hastelloy-X single edge notch specimens in which strain and temperature were varied simultaneously. Conditions were selected to include nominally elastic and nominally plastic conditions and temperatures up to 925°C. The crack growth rates were first reported as a function of the strain intensity factor (δ K _ε) derived from a crack compliance analysis. Out-of-phase (ε_max at T _max) cycling showed faster crack growth rates than isothermal or in-phase (ε_max at T _max) cycling under elastic straining. Under fully plastic cycling, the opposite results was observed, i.e. crack growth rates under isothermal cycling are faster than under TMF cycling. On a δ K _ε-basis, a strain range effect was observed. All the results were rationalized using a corrected stress-intensity factor (δ K _eff) computed from the actual load, the closing bending moment caused by the increase compliance with crack length, and with the effective opening stress. Each mode of fracture was found to be characterized by a unique crack growth rate vs δ K _eff curve. On a δ K _eff-basis, the isothermal crack growth rates at T _min and T _max provide an upper and a lower bound for the TMFCG rates. The effectiveness of δ K _eff to correlate crack growth rates under fully plastic cycling is discussed in detail.     

CRACK OPENING STRESS MEASUREMENTS OF SURFACE CRACKS IN 7075-T6 ALUMINIUM ALLOY PLATE SPECIMEN THROUGH ELECTRON FRACTOGRAPHY

Abstract— Crack opening stress measurements were carried out on 9.6 mm thick specimens of 7075-T6 aluminium alloy with semi-elliptical surface cracks. Measurements were made through a fractographic technique based on a load sequence which can produce distinct striation characteristics on the fracture surface. The crack opening stress S _op is deduced from the striation pattern. The variation of S _op along the crack periphery and during crack extension was measured. Close to the front surface S _op is higher due to plane stress condition. At a large crack depth a strong influence of plasticity in the ligament on S _op was found, i.e. S _op decreases as the crack extends to breakthrough. The agreement of d a /d N =Δ K _eff curves between surface cracks and through cracks data was only found for a limited range of crack depth of the elliptical cracks.     

Estimation of the opening load under variable amplitude loading

The crack opening/closure load concept is widely used to justify the fatigue crack growth behaviour with different load ratios and the load interaction effects. Many experimental techniques have been proposed to measure crack opening/closure load, and amongst them, compliance offset methods are widely used for their simplicity and consistency. In this paper, a modification of the ASTM method is proposed. The new method has a more general applicability as it can be applied to broadband variable amplitude loads. The method is described in detail and is applied on a 2024‐T351 aluminium alloy. The good correlation of the opening load estimated with the new method and the strip‐yield model implemented in Nasgro indicates that the new method could be used as an alternative for the cases where complex variable amplitude loads occur.     

Large crack tip deformations and plastic crack advance during fatigue

Finite-deformation elastoplastic analysis of a crack subjected to mode I cyclic loading under small scale yielding was performed. The influence of the load range, load ratio and overload on the crack tip deformations is presented. Cyclic crack tip opening displacements agreed with predictions of simpler models, where available. Crack closure was not detected. Plastic crack advance was evidenced. Its rate per cycle reproduced common trends of the fatigue cracking dependence on loading range and overload.     

Introducing the compliance ratio concept for determining effective stress intensity

Local crack tip strain measurements show that the conventional determination of ΔK effective may be misleading, especially when opening loads are relatively high as is often the case in the near-threshold regime. The conventional method assumes that K-opening can be directly related to a deviation in the linearity of a load vs crack mouth displacement curve (‘compliance offset method'). Although this deviation in linearity can be attributed to closure, local strain measurements show that significant crack tip strain can occur below the K-opening load. The redistribution of stresses associated with a partially open crack and the effect of this redistribution on the stress field in front of the crack cannot be determined simply on the basis of a change in the slope of the load–displacement curve. However, a recent addition to ASTM E-647 (Recommended Practice for Determination of Fatigue Crack Opening Load from Compliance) implies that it can. An alternative ‘compliance ratio' technique based on local crack tip strain is presented. A modification of this technique allowing the use of remote compliance measurements to account for crack tip strain below the opening load is suggested.     

The effect of crack closure on the reliability of NDT predictions of crack size

The aim of this work is to investigate the effect of crack closure on the reliability of NDT predictions of crack size. Tests are performed on mild steel plate specimens each possessing a fatigue crack. The amount of crack opening or closure is controlled using a specially built four-point bending rig. Four NDT techniques are studied: dye penetrant testing, magnetic particle inspection, AC field measurement and an ultrasonic technique using Rayleigh waves. A success/failure criterion for the reliability of sizing is adopted and both the length and depth data are analysed in accordance with this condition. It is found that both magnetic particle inspection and AC field measurement can detect and measure closed cracks but that dye penetrant testing and the ultrasonic Rayleigh-wave technique cannot detect tightly closed cracks.     

An experimental and numerical study of crack closure

Fatigue crack propagation and crack closure are studied in Al 2024-T3 under a wide range of ΔK. An elastic-plastic finite element procedure to analyze crack closure for growing cracks is presented. Numerical results are obtained for plane stress and plane strain conditions for different stress ratios. Measurements of opening loads compare well with numerical predictions within the Paris regime. Fractographic observations and compliance measurements indicate that oxide-induced and roughness-induced crack closure substantially increase the opening loads in the near-threshold regime.     

An optical-interference method for experimental stress analysis of cracked structures

An optical interference technique can be used to measure the crack opening in a cracked transparent model of a structure under load. The measured crack opening as a function of distance from the crack tip can be used in conjunction with the opening mode crack tip stress field equations to determine the opening mode stress intensity factor. Application of this method to double cantilever beam specimens comprised of two glass arms bonded together with an epoxy adhesive gave results which were in close agreement with K-calibrations based on compliance measurements. The measuring techniques and the scheme of analyzing the data could be used to obtain K-calibrations of more complex structures.     

Understanding fatigue crack propagation in AISI 316 (N) weld using Elber’s crack closure concept: Experimental results from GCMOD and acoustic emission techniques

An experimental study of fatigue crack propagation and crack closure behaviour, in compact tension specimens of AISI 316 (N) weld has been conducted. The crack closure load was determined from the changes in the slope of the load–displacement curves using global crack mouth opening displacement (GCMOD) type gauge. The results were compared with those measured by acoustic emission technique which showed good agreement with each other. The experimental data bear clear evidence of fatigue crack closure. The crack opening force was found to increase moderately with crack length and increasing R-ratio, under a constant P_max of 5 kN. Above a critical R-ratio of 0.45 (approximately), the crack closure load is smaller than the minimum applied load. A good correlation was obtained for ΔK_eff/ΔK = 0.6684 – 2.4135R + 7.0077R² in the range 0 R  0.5. The magnitude of crack closure is used to interpret observed crack growth behaviour at different R-ratios.     

SLOW FATIGUE CRACK GROWTH AND THRESHOLD BEHAVIOUR IN IMI 685

Abstract— Fatigue thresholds and crack growth rates up to 10⁻⁴ mm cycle ⁻¹ have been measured in β processed IMI 685. The results obtained in laboratory air for material having an aligned α microstructure and a random basketweave microstructure displayed a pronounced load ratio dependence which increased with decreasing ΔK. This sensitivity to mean load was also apparent from the threshold results determined in a vacuum of 5 ± 10⁻⁶ torr.
Fractographic observations, compliance measurements, pd output and crack path replication have indicated that contacts can be made between the fracture faces at a number of points behind the crack tip during the load cycle. These contacts wedge the crack open, thus preventing the stress intensity from falling to the value associated with the minimum applied load. A critical stress intensity, K _op, has been determined which relates to the crack being fully "open" and the results are reanalysed and discussed in terms of an effective stress intensity range, Δ K _eff.     

COMPATIBLE COMPLIANCE AND STRESS INTENSITY EXPRESSIONS FOR THE STANDARD THREE-POINT BEND SPECIMEN

Available expressions for load-line compliance and crack-mouth opening compliance expressions for standard three-point bend specimens (span over width ratio =4) are assessed. It is concluded that none of the available expressions are able to reproduce the source data (boundary collocation results and theoretical limits for relative crack depths equal to 0 and 1) for the entire range of relative crack depth. New expressions for example are proposed and the accuracy of each is indicated. A by-product of the new expression for load-line compliance is a new, fully compatible stress intensity expression that is, consistent with the load line compliance expression as known from theoretical considerations. Also inverse expressions are presented which predicting the crack length from compliance. To improve the accuracy of such inverse expressions, a correction that results in a considerable error reduction is presented.     

Application of the shadow optical method to fatigue and crack closure studies

In this paper it will be shown that crack closure and related crack shielding mechanisms can be studied successfully by applying the shadow optical method, also known as the method of caustics. It is shown that at least one mechanism - plasticity induced crack closure - can be identified and determined from measurements of the transverse diameter of the caustic in the crack tip region. For given fatigue conditions at which crack closure occurs, several experiments have been performed to investigate the effectiveness of the crack opening in a typical fatigue cycle.
Two different methods of closure determination have been used. A comparison is made between one of the most currently used methods of back face strain (BFS) compliance measurement and the shadow optical method (SOM). The underlying features of these two experimental techniques provide the key to finding the extent of the load in the fatigue cycles over which the crack is actually open. This redefines the value of K_min and the meaning of ΔK. The driving force, ΔK_eff is shown to be reduced in or near the fatigue threshold of the alloy, because crack closure is most effective in this part of fatigue loading. The introduction of SOM to fatigue crack closure provides a suitable alternative for finding the effective part of the stress intensity range between the minimum and maximum loads. Conclusions drawn from this work were that in addition to determining that part of the fatigue cycle over which the crack is actually open, the shadow optical method allowed an accurate interpretation of the entire fatigue cycle between K_max and K_min