EVALUATION OF KII USING A COPPER FOIL WHEN ASSESSING FRICTIONAL FORCES ON CRACK SURFACES

Abstract— The relation is examined between the strain sensitivity and the grain size of a grown copper foil gauge which has a preferred orientation to slip. We adopted this gauge to evaluate the mode II stress intensity factor K _II of a through-thickness crack in a plate subjected to cyclic torsion. The K _II values obtained are lower than the calculated values because of the frictional force on the crack surfaces. By using the experimentally determined K _II value for torsion and the calculated K _I values for plane bending, the threshold condition for crack propagation under the combination of bending and torsion is predicted on the basis of the strain energy density criterion.     

Weibull stress model for cleavage fracture under high-rate loading

This paper examines the effects of loading rate on the Weibull stress model for prediction of cleavage fracture in a low-strength, A515-70 pressure vessel steel. Interest focuses on low-to-moderate loading rates ( K˙ _I < 2500  MPa √m  s⁻¹ ). Shallow cracked SE(B) specimens were tested at four different loading rates for comparison with previous quasi-static tests on shallow notch SE(B)s and standard C(T)s. To utilize these dynamic experimental data, we assume that the Weibull modulus ( m ) previously calibrated using quasi-static data remains invariant over the loading rates of interest. The effects of dynamic loading on the Weibull stress model enter through the rate-sensitive material flow properties, the scale parameter ( σ _u ) and the threshold Weibull stress ( σ _w-min ). Rate-sensitive flow properties are modelled using a viscoplastic constitutive model with uniaxial, tension stress–plastic strain curves specified at varying plastic strain rates. The analyses examine dependencies of σ _w-min and σ _u on K˙ _I . Present results indicate that σ _w-min and σ _u are weak functions of loading rate K˙ _I for this pressure vessel steel. However, the predicted cumulative probability for cleavage exhibits a strong sensitivity to σ _u and, consequently, the dependency of σ _u on K˙ _I is sufficient to preclude use of the static σ _u value for high loading rates.     

Advances in Strain Gauge Measurement on Composite Materials

Abstract: This article gives an overview on the application of strain gauge techniques to the analysis of the strains in composite materials. The orthotropic behaviour of the composite influences the performance of strain gauges that are calibrated for use on isotropic materials. The article considers therefore the typical topics of the strain gauge technology applied to composites with particular reference to the compensation of thermal output, the measurement of the coefficients of thermal expansion, the determination of the strain and stress state, the influence of the misalignment error, the reinforcement effect, the determination of the stress intensification factor, the analysis of residual stresses by the hole drilling method and the effect of transverse sensitivity on the measurement of strains along the fibres.     

Effects of notch geometry on the local cleavage fracture stress σf

An elastic–plastic finite element method (FEM) is used to analyse the stress and strain distributions ahead of notches with various depths and flank angles in four-point bending (4PB) specimens of a C–Mn steel. By accurately measuring the distances of the cleavage initiation sites from the notch roots, the local cleavage fracture stress σ _f is measured. By increasing the notch depth and notch flank angle from 2.25 to 8.25 mm and 10 to 90°, respectively, the distributions of high stress and strain at the moment of fracture show considerable variations. However, the value of σ _f stays relatively constant. The critical fracture event is thus shown to be identical, i.e. the propagation of a ferrite grain-sized crack into the neighbouring matrix. It is concluded that σ _f is mainly determined by the length of the critical microcrack, while the notch geometry and its associated stress volume have little effect on the value of σ _f . The cleavage site ahead of a notch is determined by the stress distributions and the positions of the weakest grains.     

On the measurement of transverse sensitivity of strain gauges

The influence of the transverse sensitivity factor n on errors in the measurement of strain are discussed and it is concluded that, providing the factor n is within £0015, its effect may be disregarded in all normal applications. The determination of n on a gauge factor calibration rig is considered and an analysis made of the degree of accuracy attainable.     

THE COMBINED EFFECTS OF STRESS RATIO AND YIELD STRENGTH ON THE LEFM FATIGUE THRESHOLD CONDITION

Abstract— Long-crack (LEFM) fatigue threshold, Δ, K ₀ values are predicted which include the commonly observed effects of stress ratio, R , and yield strength, σ _y . It is assumed that the yield strength effect on threshold is indirectly related to grain size and so is not an independent variable. Two intrinsic thresholds of a material are invoked to explain the observations of higher Δ K ₀ values and a higher R -ratio sensitivity of Δ K ₀ in low strength materials compared to high strength materials. The paper shows that Δ K ₀ is almost independent of both yield strength and stress ratio at high values of the stress ratio. Quantitative relations are developed to estimate curves of (i) Δ K ₀ versus R and (ii) Δ K ₀ versus σ _y . These curves show good agreement with experimental data for steels and aluminium alloys. A method is presented that may be used as an alternative procedure for obtaining quick and conservative estimates of Δ K ₀ for design applications.     

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.     

THE ROLE OF DYNAMIC STRAIN-AGEING IN THE ENVIRONMENT ASSISTED CRACKING OBSERVED IN PRESSURE VESSEL STEELS

Abstract— The dynamic strain ageing (DSA) behaviour of A533B Class 1 reactor pressure vessel (RPV) steel, containing 5 ppm of free nitrogen, has been investigated over a wide range of strain rates from 3 × 10⁻⁷ to 3−10⁻³s⁻¹ and temperatures from 20 to 350°C. The DSA was observed within certain temperature ranges at all strain rates tested and its hardening effect in terms of the maximum strengthening stress (̀_p) decreased linearly with the increase of log strain rate. The temperature to stimulate DSA was observed to increase with increasing strain rate. The apparent activation energies of the characteristic strain rates for the onset, and peak of DSA have been determined, and their implications have been discussed. Compared with the available data, a positive effect of free nitrogen content on ̀_p has been evaluated. It has been found that the occurrence of susceptible environment assisted cracking (EAC) of A533B steel in high temperature water is co-related to the DSA behaviour. The results suggest that DSA reduces the ductility of RPV steel and its role in enhancing the EAC of RPV steels should not be neglected, in view of the coincidence with susceptibility zones for DSA and EAC in terms of strain rate and temperature.     

Assessment of the period to fatigue macrocrack initiation near stress concentrators by means of strain parameters

A new approach to the experimental assessment of the local strain at a stress concentrator has been presented. It is based on a procedure of notch opening displacement measurements at certain points in the vicinity of a notch related to the effective notch radius ρ _eff = ρ + d * , where ρ is the notch radius and d * is a material constant. Different stress concentrators in structural elements were modelled for a wide variation of notch radii ( ρ = 0.1–6.5 mm) and different geometries of specimens. Hence, a basic relationship, which directly relates the local strain range Δ ε* to the period of fatigue macrocrack initiation N _i has been established. Thus, by applying the value of Δ ε* , assessed from a direct measurement at the notch root, it is possible to determine the period N _i to initiate a fatigue macrocrack of length a _i = d * for some structural components of complicated geometry.     

Mixed-mode crack surface interference under cyclic shear loads

A previous modelling analysis predicted that crack surface interference under cyclic shear loads is a combination of cyclic shear attenuation and cyclic wedge-opening. In the present study, experimental evidence is provided on notched thin-walled tubular specimens to evaluate the modelling predictions. Tests were carried out with varied static tensions superimposed on fully reversed ( R _τ = −1) or pulsating ( R _τ = 0) cyclic shear loads. The crack surface interference was measured by near-tip strain gauge methods. Based on the single and dual strain gauge readings, the strains induced by the mode I and II interference are separately identified so that the cyclic wedge-opening behaviour was noted as a companion of the cyclic shear attenuation. The crack surface interference under cyclic shear loads is compared with the influence from varied static tensions and shear stress ratios. A comparison of the mode I crack surface interference is also made between the conditions with cyclic shear loads and cyclic tensile loads. Finally, the characteristics of crack surface displacements are discussed, and the experimental results of effective mode I and II stress intensity ranges are compared with the modelling predictions.     

DYNAMIC FRACTURE STUDY ON CrNiMoV ALLOY STEEL UNDER DIFFERENT HEAT TREATMENTS AND IMPACT RATES

Abstract— Two methods are employed, namely the Charpy impact test and a strain gauge technique, for the determination of the dynamic fracture toughnesses of CrNiMoV27 and CrNiMoV45 alloy steels under various impact loading rates and heat treatments. The results show that the dynamic fracture toughness K _Id is significantly affected by impact velocity and that tempering has a greater influence on K _Id than quenching. It is also shown that the alloy containing a greater amount of vanadium yields consistently a higher value of K _id.     

THE INFLUENCE OF STRENGTH AND STRESS RATIO ON SHORT-CRACK THRESHOLDS AND NON-PROPAGATING FATIGUE CRACKS

Quantitative predictions of the influence of yield strength and stress ratio, R , on the physically small crack fatigue threshold stress intensity, Δ K _0(s), are presented. It is shown that at R = 0 to -1, although the threshold stress Δ₀ increases, the threshold stress intensity, Δ K _0(s), decreases with increasing yield strength. Moreover, a lower bound value, Δ K _0(s)(min) is shown to have a constant value, irrespective of the strength and stress ratio. For a given strength, Δ K _0(s), decreases with increasing R in the range -1 R 0.6 and attains a constant low value for R > 0.6. Predicted values of Δ K _0(s) are in good agreement with experimental data for steels. The formation and length of non-propagating fatigue cracks, a _np, are also discussed. The methods suggested for estimating Δ K _0(s) and a _np may be found useful in design procedures.     

ON THE OVERLOAD INDUCED FATIGUE CRACK PROPAGATION BEHAVIOR IN ALUMINUM AND STEEL ALLOYS

The overload induced fatigue crack propagation behavior of several aluminum and steel alloys was examined as a function of the baseline stress intensity factor range (δ K _b). In order to gain a clearer understanding of the parameters which influence the cyclic delay phenomenon, under both plane strain and plane stress conditions, tests were conducted at δ K _b values ranging from the near threshold regime to high δ K levels approaching fast fracture. Large amounts of overload induced cyclic delay (˜100,000 cycles) were observed at both high and low δ K levels (provided the plastic zone size/thickness ratio and plastic zone size/grain size ratio approached unity, respectively) with significantly less delay occurring at intermediate δ K values. All alloys examined exhibited this type of delay behavior which can be described by a "U-shaped" plot. The delay phenomenon at high δ K _b levels under plane stress conditions was attributed to increased crack closure associated with large tensile displacements in the wake of the advancing crack. At low δ K _b levels increasing cyclic delay was attributed to an increased effective overload ratio as δ K approached δ K _th.     

THE INFLUENCE OF TEST VARIABLES ON THE FATIGUE CRACK GROWTH THRESHOLD

Abstract— A microcomputer controlled fatigue crack growth and threshold testing system has been used to investigate the influence of test variables on the measured values of Δ K _th, the threshold for fatigue crack growth, using a C-Mn steel. The work has examined: (1) the influence of crack length and test management; (2) the basic material scatter from repeated testing; (3) the effect of unloading rate C where C = (1/Δ/ K )(d Δ K /d a ); (4) the effect of step unloading; (5) the influence of minimum stress intensity factor, K _min . Comparisons have been made between the results of this computer controlled work and those published previously but made using a manual load shedding technique. The results of Δ K _th and fatigue crack growth rates are in general agreement with previous data and confirm the K _min dependence of Δ K _th and d a /d n. The value of Δ K _th is shown to be generally independent of the other test variables for a wide range of conditions and is reproducible with a low degree of scatter.     

Computer aided analysis of strain rosette data

In this paper a computer program has been developed for analysing the strain gauge rosettes by considering the transverse sensitivity of all gauges. The program is capable of calculating principal strains, maximum shear strain, principal stresses, maximum shear stress and principal directions from the data obtained by using strain gauge rosettes of various configurations. The gauge factor and transverse sensitivity of all gauges in the rosette must be the same.     

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.     

A GENERAL CRITERION FOR HIGH CYCLE MULTIAXIAL FATIGUE FAILURE

Abstract— A new simple general criterion of failure for high cycle multiaxial fatigue, τ_a/ t _A.B+σ_{n. max}/2σ_T= 1 presented. The failure criterion is based on a critical plane approach where fatigue strength is a function of the shear stress amplitude and the maximum normal stress on the critical plane of maximum shear stress amplitude. The criterion takes account of whether case A cracks, growing along the surface, or case B cracks, growing into the surface, occur. It requires knowledge of the material properties, tensile strength, σ_T, and reversed shear fatigue strength for case A, t _A, or case B, t _B, cracking, whichever is relevant. t _A is the reversed torsion fatigue strength and t _B is found from a case B cracking test case. The criterion is applicable in the region, 0.5 t ≤ t _a≤ t , and 0 ≤σ_n.max≤σ_T.     

MECHANICALLY SHORT CRACK GROWTH FROM NOTCHES IN A MILD STEEL

Abstract— Two L-notched specimens made of mild steel (average grain size =30 μm) and having root radii of 0.1 mm and 3 mm, and also a smooth surface specimen were cyclically loaded at different stress levels at R =−1 and at R = 0. A technique based on miniature strain gauges was successfully used to monitor the depth and the opening level of mechanically short cracks of depths from 0.015 mm to 0.5 mm. Three dimensional FEM computations were made to obtain appropriate calibration curves for varying crack aspect ratios and gauge eccentricities as well as notch plastic strain distributions. The fracture of L-notched specimens having a root radius of 0.1 mm was characterized by an early and multiple crack initiation phase (defined by a crack depth of 30 μm), and the short crack growth rates showed a mechanical behaviour different from that of long cracks (large discrepancies at the same Δ K -value, crack deceleration at R =−1 even beyond the notch plastic zone). For smooth surface specimens both the initiation and the propagation of a single short crack represented important fractions of the total life; the short crack growth rates were high and continuously increasing. The notch influence was highly reduced when the stress singularity is truncated by a 3 mm radius. The cracking behaviour was, in several aspects, close to that at smooth surfaces. The evolutions of crack closure were analyzed in each condition (transient decrease and stabilized value of the closure ratio U =Δ K _eff/Δ K ) and were shown to have a strong influence on short crack growth. Most of the short crack growth rates obtained in the various geometry/loading conditions are well consolidated with LEFM long crack growth rates using the Δ K _eff parameter.     

FINITE ELEMENT ANALYSIS OF SPECIMEN GEOMETRY EFFECTS ON FATIGUE CRACK CLOSURE

Abstract— Elastic-plastic finite element analysis is used to study fatigue crack closure at three different crack length to width ratios for three plane stress specimen geometries: center-cracked plate, single-edge-cracked plate (tension), and single-edge-cracked plate (bend). The maximum stress to flow stress ratio, S_max/σ_O, which successfully describes closure results in many center-cracked plate configurations, does not correlate the effect of different geometries on the normalized opening stress, S _open/ S _max. Crack opening stresses for different geometries and crack lengths are successfully correlated by a normalized stress intensity parameter, K _max/ K ₀, where K ₀=σ₀φa. The quality of the correlation is very high at small K _max/ K ₀, and gradually deteriorates as K _max/ K ₀ increases beyond the small-scale yielding regime.     

INFLUENCE FUNCTIONS FOR INCLINED EDGE CRACKS

A theoretical technique is developed for determining both KI and K_II from influence functions for angled edge cracks subjected to arbitrary distributions of normal and tangential contact stresses. Numerical results are presented which indicate the effect of crack length and crack angle on four influence functions, from which KI and K_II can be readily determined for specified distributions of tangential or normal contact stresses. In order to illustrate the use of the influence functions, a worked example is presented which shows the variation of KI and K_II with crack length and crack angle calculated for an assumed parabolic distribution of tangential stress under a fretting pad. Corresponding values of KI and K_II for other distributions of tangential and normal stresses may be determined by the same simple summation techniques used in this report.