FATIGUE CRACK GROWTH UNDER MIXED MODES I AND II

Fatigue crack growth behaviour under mixed modes I and II was studied by applying in-phase alternating tensile and torsional loading to a thin-walled hollow cylindrical specimen with an initial crack. In the linear region of a log-log plot where da/dN=A(ΔK)^m, da/dN at first decreases with increasing ΔK₁₁₀ component and then approaches a minimum close to the value of ΔK₁₁₀/ΔK₁₀～ 0.58; here ΔK₁₁₀/ΔK₁₀ is the ratio of the initial ΔK_II to the initial ΔK₁., When ΔK₁₁₀/ΔK₁₀ increases further, da/dN increases. Under shear mode, da/dN becomes higher than that under mode I. The ΔK₁, and ΔK₁₁ components during fatigue crack growth under mixed mode loading increase and decrease, respectively, with an increase in da/dN In the low crack growth rate region the fatigue crack growth rates accelerate with an increase of the initial ΔK₁₁ component, ΔK₁₁₀. Fatigue life increases with increase of ΔK₁₁₀/ΔK₁₀ under the test condition of equivalent stress range being kept constant and the pre-crack length being the same.     

Effects of an overload event on crack closure in 3-D small-scale yielding: finite element studies

This paper describes the effects of a single overload event, within otherwise constant amplitude cycles, on the plasticity‐induced closure process for mode I fatigue crack growth in the small‐scale yielding (SSY) regime. The 3‐D finite element (FE) analyses extend the initially straight, through‐thickness crack front by a fixed amount in each load cycle, using a node release procedure. Crack closure during reversed loading occurs when nodes behind the growing crack impinge on a frictionless, rigid plane. A bilinear, purely kinematic hardening model describes the constitutive response of the elastic–plastic material. Extensive crack growth in the analyses, both before and after the overload, allows the crack to grow out of the initial and the post‐overload transient phases, respectively. The work presented here shows that the large plastic deformation in the overload cycle reduces the crack driving force through enhanced closure. Further, the residual plastic deformations due to the overload cause a disconnected pattern of closure in the wake long after the crack front passes through the overload plastic zone. The computational studies demonstrate that the 3‐D scaling relationship for crack opening loads established in our earlier work for constant amplitude cycling (with and without a T‐stress) also holds before, during and after the overload event. For a specified ratio of overload‐to‐constant amplitude loading (R_OL=K^OL_max/K_max) , the normalized opening load (K_op/K_max) at each location along the crack front remains unchanged when the constant amplitude peak load (K_max) , thickness (B) and material flow stress (σ₀) all vary to maintain a fixed value of . The paper concludes with a comparison of the post‐overload response predicted by the 3‐D analyses and by the conventional Wheeler model.     

The significance of RPG load for fatigue crack propagation and the development of a compliance measuring system

In can be postulated that fatigue crack does not grow if no damage occurs in the vicinity of the crack tip. Damage may occur beyond the Re-tensile Plastic zone's Generated load (RPG load) in the vicinity of a crack tip under loading process. We propose an effective stress intensity factor range ( K _RP) corresponding to the period in which the re-tensile plastic zone appears, in place of K _eff proposed by Elber [1], for a fatigue crack propagation parameter.We then consider the small change of compliance for a cracked body under cyclic loading, for the purpose of measuring RPG load as well as crack opening load and crack closing load. Moreover a subtraction circuit which can measure the small change of compliance during fatigue test is developed and an automatic controlled system which can control the adequate values of resistance in the circuit and the output voltage range from strain amplifiers for minimizing relative noise level is also developed. Then fatigue crack propagation tests of CT specimens were carried out with various stress ratios of constant amplitude loadings. Moreover K _th tests with the conditions of constant stress ratio and constant maximum load with increasing stepwise minimum load were also carried out. It becomes clear that the logarithmic curve of K _RP—crack propagation rate appears to be linear in a wide range from the region of very slow growth rate to the region of stable growth rate. On the other hand, threshold phenomenon appears only circumstantially due to the particular loading pattern on K _eff based on the crack opening load and K _eff ^cl based on the crack closing load. Moreover K _RP gives the quantitative effect of stress ratio on fatigue crack propagation rate.     

SMALL FATIGUE CRACK GROWTH BEHAVIOUR UNDER TWO STRESS LEVEL MULTIPLE LOADING

Small fatigue crack growth behaviour in a low alloy steel was investigated under two stress step multiple loading in which the secondary stress was below the fatigue limit. Crack growth rates were presented in terms of a stress intensity factor and compared with data obtained under constant amplitude loading. In the higher ΔK region, crack growth rates increased monotonously with increasing ΔK even though the stress level was below the fatigue limit, and tended to be lower than those for constant amplitude loading. In the lower ΔK region, cracks showed a complicated behaviour, that is, an initial high growth rate was observed followed by an arrest or a drop to a minimum value and then a gradual increase. The average crack growth rates per cycle at both primary and secondary stresses in each block were approximately consistent with the da/dn-ΔK relation for constant amplitude loading. A suggestion for the prediction of crack growth life is given.     

Creep Crack Growth in Polyethylene Under Combined Mode I and Mode II Loading

Creep crack growth characteristics under various combined mode I and mode II loadings were studied using the compact tension shear (CTS) specimens of polyethylene. Creep crack growth rates da/dtunder combined mode I and mode II loading can be correlated with a single effective stress intensity factor K _Ieffderived from the combined — mode fracture toughness envelope. The steady state or constant crack growth rates which occupy the significant part of creep failure life increase with the increasing initial effective stress intensity factor.     

A new push‐pull sample design for microscale mode 1 fracture toughness measurements under uniaxial tension

A sample geometry is proposed for performing microscale tensile experiments based on a push‐pull design. It allows measuring mode 1 fracture toughness under uniform far‐field loading. Finite element simulations were performed to determine the geometry factor, which was nearly constant for Young's moduli spanning 2 orders of magnitude. It was further verified that mode 1 stress intensity factor K_I is nearly constant over the width of the tension rods and an order of magnitude higher than K_II and K_III. Notched samples with different a/w ratios were prepared in (100)‐oriented Si by a combination of reactive ion etching and focused ion beam milling. The mode 1 fracture toughness K_I,q was constant with a/w and in average 1.02 ± 0.06 MPa√m in good agreement with existing literature. The geometry was characterized and experimentally validated and may be used for fracture toughness measurements of all material classes. It is especially interesting when a uniaxial, homogeneous stress field is desired, if crack tip plasticity is important, or when positioning of the indenter is difficult.     

Mixed-mode high temperature toughness of silicon nitride

Both opening-mode and mixed-mode fracture toughness tests were carried out at 1200 and 1300 °C on a sinter/HIP grade of silicon nitride. Data for pure opening loading (K _Ic) agree well with other experiments on the same material, which showed that the toughness was lower at 1000 °C than at room temperature, but increased as temperature increased above 1000 °C. The ratio of K _IIc/K _Ic was sufficiently insensitive to temperature that it can be considered to be constant. Results are discussed in the context of mechanisms that have been proposed to explain fracture toughness in silicon nitride.     

NON-PROPAGATION CONDITIONS (ΔKth) AND FATIGUE CRACK PROPAGATION THRESHOLD (δKT)

Abstract— Fatigue crack propagation threshold values have been determined with two experimental methods, it., the constant R method and the constant K_max method. Three materials, namely A17075-T7351 and Ti6A14V STA in the LT- and TL-orientations, and a Ti-turbine disk material (IMI 685) in the CR-orientation, were investigated. The paper is divided into 3 parts. In the first part the test conditions, the experimental results and the conclusions drawn from the experimental results are presented, namely that the three different functional dependencies of ΔK_th on R cannot be reconciled with present continuum mechanics concepts. In the second part, some facts used in conjunction with the da/dN–ΔK_eff methodology are applied to the non-propagation condition ΔK_th. Parameters such as K_Op, the threshold ΔK_T, and a parameter “K_LL” are investigated by numerical modelling of their individual influence on the ΔK_th versus R curves. This modelling work shows that the individual ΔK_th versus R curves are primarily dependent on the K_op behavior of the respective material. Further, it is shown that the threshold ΔK_T is a constant value, independent of any particular cyclic loading condition. In the third part of the paper, the ΔK_eff concept is applied to the experimental results obtained in the first part. Using either experimentally or semi-empirically determined K_op functions and the measured ΔK_T values, the ΔK_th versus R curves of the three materials investigated were accurately reconstructed. It follows that the ΔK_th versus R curves of the individual materials are the natural consequence of the driving force for fatigue crack propagation, namely ΔK_eff     

Promotion effect of nanosized Pt,RuO2 and NiOx loading on visible light-driven photocatalysts K4Ce2M10O30 (M = Ta,Nb) for hydrogen evolution from water decomposition

Metal oxide photocatalysts K₄Ce₂M₁₀O₃₀ (M = Ta, Nb) capable of responding to visible light were synthesized by conventional high temperature solid-state reaction. The photocatalysts have an appropriate band gap energy ca. 1.8–2.3 eV and excellent chemical potential level to evolve H₂ from aqueous solutions containing a sacrificial electron donor (Na₂SO₃) under visible light irradiation (λ>420 nm) without any co-catalyst. When they were loading with Pt, RuO₂ and NiO_x, the activities for evolving H2 were prompted markedly. By SEM and TEM investigations, it can be seen that these loading K₄Ce₂M₁₀O₃₀ (M = Ta, Nb) in diameter of about 10–30nm particles, especially the NiO_x loading even formed double layered structure with metal nickel (Ni) and metal oxide (NiO). The reasons for the increasing activities after these loading electron migrating from the conduction band of K₄Ce₂M₁₀O₃₀ (M =Ta, Nb) to the Pt, RuO₂ and NiO_x nanoparticles, which function as H₂ production sites on the surface of catalysts. The same phenomenon appears on the solid solution K₄Ce₂Ta_{10 –x}Nb_xO30 (x = 0–10) with loading RuO₂.     

Analysis of crack propagation using ΔK and Kmax

In this investigation a general relationship between fatigue crack growth rate, da/dN, and a two-parameter ΔK and K_max driving force is derived using fundamental fatigue (ε–N curve) properties. A power-law relationship between ΔK and K_max is obtained by relating the crack growth rate to the fatigue life of the ‘process zone’. Theoretically, there are four different regions on a log–log plot depending on the particular combinations of ΔK and K_max. The actual analysis of experimental data indicates only two different regions namely, ΔK and K_max dominated, corresponding to high and low load ratios, respectively. A new way of representing the da/dN data in terms of ΔK and K_max by means of the crack propagation (CP) table is proposed. Finally, the application of the CP table for predicting crack growth rate under constant amplitude loading is explained and discussed.     

Shear mode threshold for a small fatigue crack in a bearing steel

The fatigue behaviour of small, semi‐elliptical surface cracks in a bearing steel was investigated under cyclic shear‐mode loading in ambient air. Fully reversed torsion was combined with a static axial compressive stress to obtain a stable shear‐mode crack growth in the longitudinal direction of cylindrical specimens. Non‐propagating cracks less than 1 mm in size were obtained (i) by decreasing the stress amplitude in tests using notched specimens and (ii) by using smooth specimens in constant stress amplitude tests. The threshold stress intensity factor ranges, ΔK_IIth and ΔK_IIIth, were estimated from the shape and dimensions of non‐propagating cracks. Wear on the crack faces was inferred by debris and also by changes in microstructure in the wake of crack tip. These effects resulted in a significant increase in the threshold value. The threshold value decreased with a decrease in crack size. No significant difference was observed between the values of ΔK_IIth and ΔK_IIIth.     

Generation and analysis of FCG data using a single specimen and Kmax–ΔK testing matrix

A custom method to generate fatigue crack growth (FCG) data requires testing of multiple specimens at different load ratios, R, and the application of a load shedding procedure from pre-cracking level to threshold. In this paper, a novel method of testing has been investigated which utilizing a single specimen and a testing matrix in terms of K_max and ΔK values corresponding to predetermined R-ratios for which FCG data are recorded. Automatic K-controlled tests on 2324-T39 Al alloy were conducted using both increasing and decreasing ΔK procedures while K_max was kept constant. Results show that the increasing ΔK procedure gives less scatter than decreasing ΔK procedure. Also, fatigue crack growth curves near the threshold region obtained from increasing ΔK are above the curves obtained from decreasing ΔK procedure. These differences are explained by means of interaction between cyclic plastic zones and their effect on fatigue damage. The procedure with increasing ΔK demonstrated minimal interaction effects and hence it is recommended for efficient FCG data generation. The proposed procedure reduces testing time, the overall scatter associated with multiple samples and eliminates possible uncertainty linked to the load shedding procedure and its effects on threshold.     

Fracture behaviour of glass-fibre mat-reinforced structural nylon RIM composites studied by microscopic and acoustic emission techniques

The fracture and failure behaviour of continuous glass-fibre mat-reinforced nylon block copolymer were studied at monotonic increased loading at different temperatures (T=–40 to 80 °C and deformation rates (v=1 and 1000 mm min^–1). The fracture toughness,K _c, was determined on compact tension specimens of different size in order to elucidate size effects.K _c increased with increasing glass-fibre mat content and with deformation rate, whereas increasing temperature resulted in lowerK _c values.K _c was unaffected by the free ligament width of the compact tension specimens used. The failure manner was studied by acoustic emission and microscopic techniques (transmitted light and scanning electron microscopy). Simultaneous monitoring of the failure mode by acoustic emission and transmitted light microscopy allowed the failure sequence to be deduced and led to a reliable discrimination between the observed failure events based on their acoustic emission signal characteristics (e.g. amplitude, energy). For this composite with a very ductile thermoplastic matrix the following failure steps were concluded: (a) fibre debonding due to crack-tip blunting, (b) network-type deformation of the glass-fibre mat with concomitant fibre debonding and voiding of the matrix, (c) formation of kinked strands with crack opening due to matrix yielding, (d) fracture of the bent filaments within the strands followed by pull-out processes (fibre-fibre, fibre-matrix). The development of the damage zone was also assessed by acoustic emission via localization of the related events. It was established that the damage zone reaches its maximum dimension at the maximum load and only its shape changes along the crack-growth direction upon further loading.     

Physical meaning of ΔKRP and fatigue crack propagation in the residual stress distribution field

Previous papers have shown ΔK_RP to be a useful parameter describing fatigue crack propagation behavior, where ΔK_RP is an effective stress intensity factor range corresponding to the excess RPG load (re-tensile plastic zone's generated load) in which the retensile plastic zone appears under the loading process. In this paper, the relationship between ΔK_RP and the zone size ( ) (which is smaller between the tensile plastic zone at maximum load and the compressive plastic zone at minimum load) was investigated using a crack opening/closing simulation model so as to consider a physical meaning of ΔK_RP. As a result, it becomes clear that ΔK_RP dominates the zone size where fatigue damage mostly occurs. This result supports the following crack propagation equation

where C and m are material constants.Simulation and fatigue crack propagation tests were then carried out for compact tension (CT), center cracked tension (CCT) and four points bend (4PB) specimens under constant amplitude loading to obtain C and m values for HT-50 steel. Fatigue crack propagation tests were also carried out under constant amplitude loading using CCT specimens with residual stress distribution due to flame gas heating at the center line or edge lines. The T specimen introduced tensile residual stress at the tip of a notch, and the C specimen introduced compressive residual stress. It therefore becomes clear that tensile residual stress leads to a decrease in RPG load, while compressive residual stress leads to increase in RPG load, and that the simulation results are in good agreement with the experimental RPG load. It also becomes clear that simulated crack growth curve using the simulated and the above equation is in good agreement with the experimental curve. It is understood that tensile residual stress creates only a slight increase in crack propagation rate and compressive residual stress create a big decrease a crack propagation rate.     

Tensile fracture of centre-notched angle ply (0/±45/0)S and (0/90)2S graphite — epoxy composites

The fracture behaviour of centre-notched (0/± 45/0)_S and (0/90)_2S laminates with increasing notch length has been studied. Two test series have been investigated: specimens of constant width (W=20 mm) and small notch length (2a 12 mm), and specimens with various notch lengths (5 2a 35 mm) and a constant relative notch length (2a/W=0.5). An X-ray technique showed that the damage at the notch tip, which is formed at increasing load, consists mainly of subcracks parallel to the fibres of the constituent layers. The damage zone causes the crack opening displacement (COD) to deviate from the original linearity. TheK _R curve concept has been applied assuming that the COD deviation from linearity is completely the result of original crack extension. This approach fails to describe the notch length effect, because a tangent point between theK _R andK curves was not found and because of a strong dependency of the maximum fracture resistanceK _Rmax on notch length. The fracture behaviour of 20 mm wide specimens could be explained with the point and average stress criteria, based on characteristic lengths which are independent of notch length. At various notch lengths at a constant 2a/W=0.5, however, the characteristic lengths increased with increasing notch length.     

Fatigue crack propagation in API 5L X‐70 pipeline steel longitudinal welded joints under constant and variable amplitudes

Fatigue crack propagation (FCP) under constant and variable amplitude loading in base metal (BM), weld metal (WM) and heat affected zone (HAZ) of longitudinal welded joints of an API X‐70 pipeline steel was investigated. Constant amplitude loading tests were performed at R = 0.1 and 0.5, whereas for variable amplitude testing single peak tensile overloads (OLs) alternating between 75 and 100% of maximum load were applied at 2.5 mm intervals in crack growth. Results of SE(B) specimens tested under constant and variable amplitude loading revealed that BM, WM and HAZ regions subjected to R = 0.5 and low ΔK‐values presented the highest crack growth rates. At higher ΔK values FCP rates in all the studied regions were similar and the R effect on FCP rate was no more observed. Crack growth retardation due to OLs was observed at the three studied regions, showing a decrease on the FCP delay with a decreasing on ΔK.     

Effect of Strain Rate and Preloading on the Fracture Toughness of ZrO2-Based Ceramics

We study the variation of the fracture toughness K_Ic ofZrO₂ - Y₂ O₃ ceramics (density 98%) as a function of the testing machine crosshead speed (0.005–50 mm/min) and preloading at K_I < K_c. The fracture toughness is shown to be practically constant in the speed range from 0.05 to 5 mm/min. At a loading rate of 50 mm/min, the quantity K_Ic substantially decreases (by a factor of more than two), whereas at a rate of 0.005 mm/min it slightly increases. Preloading leads to a 1.5-fold increase in K_Ic. Variation of the fracture toughness is associated with structural transformations.     

Crack significance evaluation with special reference to welded structures

Fracture mechanics parameters (stress intensity factorK _I and its critical valueK _Ic , crack opening displacement, and the contourJ integral) are originally defined for static and quasistatic loading conditions. On the basis of theoretical background, standard test methods for the experimental determination of their specific values were developed. Structural integrity analysis requires the extension of application of these parameters to other types of loading. We propose new parameters for stress corrosion (stress corrosion cracking thresholdK _1sco ), for cyclic loading (stress intensity factor range ΔK and fatigue threshold ΔK _th), and for creeping at elevated temperatures (C ^* andC _t integrals). The structural integrity of welded structures is mainly affected by cracks in welded joints. We demonstrate the practical application of fracture mechanics parameters to the evaluation of structural integrity under the above-mentioned loading conditions. Faculty of Technology and Metallurgy, University of Belgrade, Yugoslavia. Faculty of Mechanical Engineering, University of Belgrade, Yugoslavia. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 2, pp. 107–118, March–April, 1996.     

A numerical model for calculation of stress intensity factors in particle-reinforced metal–matrix composites

A two-dimensional finite element model was developed to study effects of particle diameter, mechanical properties of the fiber and matrix materials and loading conditions (Mode 1 and Mixed-Mode). A theoretical model was proposed to calculate the stress intensity factor for an interface crack in Particle-Reinforced Metal–Matrix Composites. The displacement Correlation Method was used to calculate the stress intensity factors K ₁ and K ₂. In the present model the fiber and matrix materials were modeled in linear elastic conditions. The interface crack was considered between the fiber and matrix, without the presence of the interphase. Obtained results show that the key role on the stress intensity factors played by the relative elastic properties of the fiber and matrix. The results also show that K ₁ and absolute K ₂ values increase for both Mode 1 and mixed-mode loading condition once Young’s modulus of the fiber material increases. The values of K ₁ and K ₂ stress intensity factors decrease when the fiber volume fraction increases for Mode 1 loading.     

Influence of Punch Velocity on the Compressibility of Granules

Abstract

The influence of punch velocity over the range 1-30 mm/min on the compressibility of granules and particles was studied using a modified Kawakita equation. Granule strength (S_t) increased with increasing concentration and viscosity of binder solution as well as increasing mean molecular weight of binding agent. The compressibility of powders was evaluated by the modified Kawakita equation (K). For the granules, the relationship between pressure and reciprocal of porosity (I/ε) showed an inflection point, but for the particles, no such inflection point was found. The slope of low compression stress in the stage of densification by powder slippage and rearrangement was the constant K₁; and slope of high compression stress in the stage of elastic, plastic deformation and plastic fracture of particles was the constant K₂. The K₁ values decreased with increasing punch velocity. An approximately linear relationship was observed between reciprocal of compressibility constant (I/K₂) and granule strength (S_t). For crystalline lactose, K values decreased with increasing punch velocity, indicating that compressibility was lowered. Thus, compressibility was shown to be dependent on type of crystal. The quantity of stress relaxation increased with increasing punch velocity. Especially, constant a and b values in a cellulose system (HPC) were greater than those in a noncellulose system (PVP). As a good relationship was found between constants a, b and constant K₂, materials which undergo plastic deformation and fragmentation have great stress relaxation. The radial tensile strength (σ_t) increased with increasing granule strength (S_t). We concluded from these findings that the σ_t value was affected by the contact area rather by than the number of contact points.