A study of crack closure under constant amplitude loading for 6063-T6 Al-alloy

Crack closure experiments were performed on 6063-T6 Al-alloy, using a COD gauge for various load ranges (Δp) and stress ratios, R. On the basis of the experimental results a model for effective stress intensity range ratio U was developed. This model was found to be a function of the stress ratio, R, and was fitted to existing constant amplitude crack propagation data for 6063-T6 Al-alloy. The crack closure load stabilized after 1 mm initial crack growth.     

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.     

Experimental observation of crack propagation in 6063-T6 al-alloy under constant amplitude loading

Crack propagation experiments were performed on 6063-T6 Al-alloy for various load ranges and stress ratios. Experimental results show that for a constant load range, the life of specimens decreased as stress ratio increased. At constant maximum load, the life of the specimen increased as the load ratio increased. The crack growth data were analysed in terms of ΔK_eff as a function of stress ratio R. The data covered R values from 0 to 0·5 and a good relationship was obtained for K_eff/K = 0·55 + 0·12 R². A crack growth rate equation was developed.     

Investigation of yield strength and single cycle overload on crack closure

Crack closure experiments were performed on 6063-T6 and 6061-T6 aluminium alloys, using a crack opening displacement gauge, for various overload ratios (1·67, 1·88 and 2·06). On the basis of these experiments some relationships are developed. The delay period after application of a single overload increases with increase in the magnitude of overload. The retardation is decreased with increase in prestrain for the same overload ratio. After the overload cycle the increase in U values is less in prestrained material than in the as-received material. Crack growth rate also decreases after application of an overload cycle; it attains a constant amplitude crack growth rate and crack closure value after a certain number of cycles. For the same stress ratio, the delay period in the 6063-T6 alloy was found to be more than in the 6061-T6 alloy. The experimental results when plotted on log-log graph paper, show that N_D/N_CAL vs overload ratio and crack length (when U = U_min) vs overload ratio fit a straight line, from which the power laws are developed.     

Crack propagation rate as a function of crack tip characteristics

The dependence of crack growth rate on various crack tip parameters was studied. Experiments were performed on thin sheets of 6063-T6 Al-alloy having a central notch, to find crack tip opening displacement, total strain range, plastic strain range, crack opening stress and crack growth rate. Crack tip opening displacement and crack opening stress were measured, using a surface measurement technique, with small crack opening displacement gauges. The theoretical predictions of crack tip opening displacement compare fairly well with the experimental values. It is found that crack propagation rate vs total strain range-plastic strain range gives a straight-line fit on a log-log graph and, for positive stress ratios, the fatigue crack growth rates are found to be independent of R.

Experimental results show that the crack opening stress is not affected by the position of the gauge when it is mounted behind and near the crack tip.

The effect of mechanical properties and loading on crack growth were also studied. The specimens were fatigue cracked to a predetermined length and some specimens were annealed and again loaded cyclically. The application of cyclic loads to annealed specimens caused significant increase in crack propagation rates in comparison with the specimens having no heat-treatment. The load-displacement record was found to stabilize in about 10 cycles; the crack then extended slowly as a fatigue crack. Crack propagation rates for different values of R for annealed and work-hardened material were plotted against a crack tip parameter, ΔK*, based on notional crack lengths. Since the results of da/dN vs ΔK* for both states of material (as-received and annealed) seem to lie on the same straight line on a log-log graph, the study provides a hope that the results for a material tested in any state (annealed or work-hardened) for positive values of R (0·0≤R≤0·3) will lie on this line, thus eliminating fatigue tests on the same material under different work-hardening conditions for different values of R. Models for da/dN have been developed using various crack tip parameters.     

A study of effective stress range ratio in programmed loadings

Crack closure experiments were performed on 6061-T6 and 6063-T6 Al alloys for Lo-Hi and Hi-Lo programmed loadings. In these experiments each block of overload was continued to propagate up to 2 mm crack length. In the Lo-Hi load sequences the closure load increases but the value of U remains the same. The crack growth rate accelerated due to larger value of ΔK. The values of U stabilized in about 10 cycles for each block. In Hi-Lo load sequences, retardation takes place. The closure load increases and becomes stabilized in 10 cycles. It remains constant for a number of cycles and reaches its CAL closure value.     

Calculation of stress intensity factors for semielliptical cracks in a thick-wall cylinder

Weight functions for the surface and the deepest point of an internal semielliptical crack in a thick-wall cylinder were derived from a general weight function and two reference stress intensity factors. For several linear and nonlinear crack face stress fields, the weight functions were validated against finite element data. Stress intensity factors were also calculated for the Lamé through the thickness stress distribution induced by internal pressure. The weight functions appear to be particularly suitable for fatigue and fracture analysis of surface semielliptical cracks in complex stress fields. All stress intensity factor expressions given in the paper are valid for cylinders with an inner radius to wall thickness ratio, R_i/t = 4.     

Effect of variable single cycle peak overload on fatigue life

Crack propagation experiments were conducted on 6061-T6 Al-alloy, for various overload ratios (1·75, 2·00, 2·15, 2·25 and 2·5). On the basis of these experiments a power law is developed to predict the delay period. The delay period after the application of a single overload increases as the magnitude of overload increases. Crack growth decreases after the application of an overload cycle and after a certain number of cycles it tends to attain its CAL crack propagation rate.     

Numerical simulation of tearing–fatigue interactions in 316l(N) austenitic stainless steel

The loading history of engineering components can influence the behaviour of defects in service. This paper presents, the results of a numerical study aimed at using the Gurson ductile damage model, calibrated against J R-curve data, to simulate load-history effects on ductile tearing behaviour in austenitic materials. The work has demonstrated that ductile crack growth resistance is influenced by sub-critical crack growth by an intervening mechanism such as fatigue. Fatigue crack growth under a positive R-ratio leads to increase in subsequent tearing resistance through three main mechanisms: (i) re-sharpening of the crack tip; (ii) crack extension through the fracture process zone; and (iii) cyclic loading effects on void development. The ratio of minimum to maximum stress during fatigue loading (R-ratio) has been shown to influence subsequent tearing resistance, with an R-ratio of 0.2 generally leading to a greater enhancement in tearing resistance than an R-ratio of 0.1. This behaviour is due to the influence of R-ratio on void development ahead of the fatigue crack tip. Finally, relevant experimental data compare favourably with the predicted J R-curves.     

A weight function approach to stress-intensity factors for half-elliptical surface cracks in cylindrical pressure vessels subjected to thermal shock

Root-mean-square averaged (RMS-averaged) stress-intensity factors were calculated for internal half-elliptical surface cracks in cylindrical vessels using a weight function method. The weight function was derived based on an approximate crack surface displacement representation. Stress-intensity factors for longitudinal half-elliptical inner surface cracks subjected to polynomial stress distribution have been presented and compared favorably with the existing numerical solutions. Superposition of the polynomial stress-intensity factors has provided an extremely efficient solution to the thermal shock crack problems. The crack geometries analyzed were R_i/R₀ = 10/11 and 4/5, a/c = 0·3333 and 0·8, the ratio of crack depth to wall thickness ranged from 0 to 0·8. The results, as well as the proposed method, offer a very powerful and economic way for the safety assessment of pressure vessels subjected to complex and varying load conditions.     

Finite element based evaluation of stress intensity factors for interactive semi-elliptic surface cracks

A finite thickness plate with two coplanar self-same shallow and deep semi-elliptical surface cracks subjected to remote tensile surface traction is considered for fracture analysis. Based on three-dimensional (3D) finite element solutions, stress intensity factors (SIFs) are evaluated along the entire crack front using a force method. The line spring model has also been used to evaluate crack depth point SIFs using shell finite element analysis. A wide range of geometric dimensions and crack configurations viz. crack shape aspect ratio (0.3≤a/c≤1.2), crack depth ratio (1.25≤t/a≤6), relative crack location (0.33≤2c/d≤0.9) and normalized location on the crack front (0≤2φ/π≤2) are considered for numerical estimation of crack interaction factors. SIFs evaluated at the depth point using the force method from the 3D finite element results are compared with SIFs evaluated using the line spring model. Finally, using finite element results, an empirical relation is proposed for the evaluation of crack interaction factors. For the ranges considered, the proposed empirical relation predicts crack interaction factors at critical locations within ±2% of the 3D finite element solutions.     

Effect of temperature on the threshold fatigue crack growth behaviour of spheroidal graphite cast iron

The influence of temperature at various R ratio values on the fatigue crack propagation response of a ferritic spheroidal graphitic cast iron has been studied. It has been established that the influence of R ratio on ΔK_th is strongly dependent upon the test temperature. At elevated temperatures the influence of R ratio is significantly less than that at ambient temperature. At low to intermediate R ratio values temperature initially decreased, then, with increasing temperature, increased the ΔK_th levels, causing a minimum in ΔK_th to occur at 250–300°C. At high R ratio, however, ΔK_th exhibited a small but consistent increase with temperature. The influence of temperature on the ΔK_th at various R ratio values could be adequately explained in terms of crack closure. Much intergranular failure was observed on the fatigue fracture surfaces at ambient temperature, whereas at elevated temperatures there was little evidence of this particular failure.     

A comparison of methods of calculating stress intensity factors for cracks in pipes and thin walled cylinders

This paper presents results of a study undertaken to compare stress intensity factor solutions for various crack geometries in pipes and thin walled cylinders against the equivalent flat plate K solutions. The exercise was restricted to cylinders and pipes with wall thickness to radius ratios (t/R) of 0·1.

The results of the exercise indicate that structural integrity assessments of pipes and thin walled cylinders which contain flaws should ideally incorporate representative stress intensity factor solutions. Nevertheless there are a number of crack geometries for which flat plate K solutions can provide reasonable estimates of the stress intensity factor.     

Study on the influence of magnitude and instant of overload on fatigue

Experiments on single tensile overload applied at different crack length were performed on 6063-T6 Al alloy. Experimental results show that increasing the magnitude of overload increases crack growth retardation. It was also found that crack growth retardation decreases when overload is applied at larger crack length. A model for finding the number of delay cycles by considering overload ratio and instant of overload is developed.     

On the evaluation of crack propagation velocity by the observation of stress waves created during tensile fracture

The purpose of the work described in this paper is to study the relation of crack propagation velocity to stress variation arising due to the arrival of a longitudinal unloading wave created during a tensile fracture. The time dependent stress due to the compression wave emanated from the rupture section of the notched round bar specimen of annealed JIS-SS41 steel is observed using the strain gage method. The same problem is theoretically analyzed by postulating three different crack growth models. A crack front of circular shape possessing a radius which increases at a constant rate (c_o/k) with time is assumed, where c_o is the propagation velocity of the elastic stress wave and k is the crack velocity factor determined by comparing the experimental results with the theory.     

Influence of applied stress ratio on fatigue crack growth in 6063-T6 aluminium alloy

Crack growth data of 6063-T6 sheet material were analysed with different formulas for ΔK_eff as a function of stress ratio R. The data covered R values from 0·1 to 0·5. A good correlation was obtained for $\text{d}\text{a}\text{d}\text{N}$ and ΔK_eff using the Schijve⁶ equation for U.     

Solar DHW system performance correlation revisited

The long-standing question of the most appropriate dimensionless groups to be used for the correlation of the performance of solar domestic hot water (SDHW) systems is reviewed. It is shown that first principles enable two groups to be defined which collapse both the correlations of Kenna and f-chart to a single curve, for a given ratio R of the daily demand to storage mass. These are the groups that determine the initial gradient of the curve and its final asymptote. Using a thermal model of the collector–store combination, it is then shown how the shape of the remainder of the correlation curve also derives from basic physical principles. This model provides a convenient instrument for illustrating the sensitivity of system performance to the many factors that affect it. Some, such as the shape of the irradiance pattern at the collector, are found to be relatively weak. It is further shown why systems with differing values of R cannot be represented by a single correlation curve. However, a set of coordinates are suggested which nearly collapse the curves for variable R, providing a convenient format for presenting correlations of simulated or measured data for use in long-term performance prediction and the checking of performance claims.     

Hydrogen trapped at intermetallic particles in aluminum alloy 6061-T6 exposed to high-pressure hydrogen gas and the reason for high resistance against hydrogen embrittlement

Hydrogen (¹H) trapped at intermetallic particles (IPs) in an aluminum alloy, 6061-T6, was visualized with secondary ion mass spectrometry (SIMS) by precisely excluding the false signal which is caused by background hydrogen (H_BG). The interference of the H_BG was avoided by a unique continuous pre-sputtering (pre-digging) by a primary ion beam of SIMS into a sample in combination with silicon sputtering prior to the SIMS measurement of the sample and we succeeded in visualizing the exact signal of ¹H trapped by IPs at subsurface layer of the sample charged in high-pressure hydrogen gas. The thermal desorption analysis clarified that the desorption energy (E_d) of the IPs was 200 kJ/mol or higher, which was extremely higher than E_d for lattice interstice, dislocations, and vacancies. High density hydrogen was concentratedly trapped at IPs in the subsurface layer in contact with the hydrogen gas. This nature causes an extremely low effective hydrogen diffusivity of 6061-T6 of the order of 10^?14 m²/s even at 200 °C and may eventually give a high HE resistance to 6061-T6.     

Effect of constraint on ductile crack growth and ductile-brittle fracture transition of a carbon steel

Ductile-brittle fracture transition was investigated using compact tension (CT) specimens from −70 to 40°C for a carbon steel. Large deformation finite element analysis was carried out to simulate the stable crack growth in the compact tension (CT, a/W = 0.6), three point-point bend [SE(B), a/W = 0.1] and centre-cracked tension [M(T), a/W = 0.5] specimens. An experimental crack tip opening displacement (CTOD) resistance curve was employed as the crack growth criterion. Ductile tearing is sensitive to constraint and tearing modulus increases with reduced constraint level. The finite element analysis shows that path-dependence of the J-integral occurs from the very beginning of crack growth and ductile crack growth elevates the opening stress on the remaining ligament. Cleavage may occur after some ductile crack growth due to the increase of opening stress. For both stationary and growing cracks, the magnitude of opening stress increases with increasing in-plane constraint. The ductile-brittle transition takes place when the opening stress ahead of the crack tip reaches the local cleavage stress as the in-plane constraint of the specimen increases.