Mode I fatigue crack growth under biaxial loading

This paper is centred on the role of the T-stress during mode I fatigue crack growth. The effect of a T-stress is studied through its effect on plastic blunting at crack tip. As a matter of fact, fatigue crack growth is characterized by the presence of striations on the fracture surface, which implies that the crack grows by a mechanism of plastic blunting and re-sharpening (Laird C. The influence of metallurgical structure on the mechanisms of fatigue crack propagation. In: Fatigue crack propagation, STP 415. Philadelphia: ASTM; 1967. p. 131–68 [8]). In the present study, plastic blunting at crack tip is a global variable ρ, which is calculated using the finite element method. ρ is defined as the average value of the permanent displacement of the crack faces over the whole K-dominance area. The presence of a T-stress modifies significantly the evolution of plastic deformation within the crack tip plastic zone as a consequence of plastic blunting at crack tip. A yield stress intensity factor K_Y is defined for the cracked structure, as the stress intensity factor for which plastic blunting at crack tip exceeds a given value. The variation of the yield stress intensity factor was studied as a function of the T-stress. It is found that the T-stress modifies significantly the yield point of the cracked structure and that the yield surface in a (T, K_I) plane is independent of the crack length. Finally, a yield criterion is proposed for the cracked structure. This criterion is an extent of the Von-Mises yield criterion to the problem of the cracked structure. The proposed criterion matches almost perfectly the results obtained from the FEM. The evolution of the yield surface of the cracked structure in a (T, K_I) plane was also studied for a few loading schemes. These results should develop a plasticity model for the cracked structure taking into account the effect of the T-stress.     

The jump-like crack growth model, the estimation of fracture energy and JR curve

In this paper the jump-like crack growth model for monotonic loading is applied to re-examine both the onset of crack growth and process of stable crack growth. In the former case the fracture energy associated with a new surface creation is estimated and the in-plane constraint influence on this quantity is examined using the J-A₂ approach. In the later case the formula to compute the J-resistance curve is re-examined and compared with the one known from the standards. In the analysis the plane strain model of a structural element made of elastic-plastic material is assumed.     

Constraint-modified J−R curves and its application to ductile crack growth

The concept of J-controlled crack growth is extended to J–A ₂ controlled crack growth using J as the loading level and A ₂ as the constraint parameter. It is shown that during crack extension, the parameter A ₂ is an appropriate constraint parameter due to its independence of applied loads under fully plastic conditions or large-scale yielding. A wide range of constraint level is considered using five different types of specimen geometry and loading configuration; namely, compact tension (CT), three-point bend (TPB), single edge-notched tension (SENT), double edge-notched tension (DENT) and centre-cracked panel (CCP). The upper shelf initiation toughness J _IC, tearing resistance T _R and J–R curves tested by Joyce and Link (1995) for A533B steels using the first four specimens are analysed. Through finite element analysis at the applied load of J _IC, the values of A ₂ for all specimens are determined. The framework and construction of constraint-modified J–R curves using A ₂ as the constraint parameter are developed and demonstrated. A procedure of transferring the J–R curves determined from standard ASTM procedure to non-standard specimens or practical cracked structures is outlined. Based on the test data, the constraint-modified J–R curves are presented for the test material of A533B steel. Comparison shows the experimental J–R curves can be reproduced or predicted accurately by the constraint-modified J–R curves for all specimens tested. Finally, the variation of J–R curves with the size of test specimens is produced. The results show that larger specimens tend to have lower crack growth resistance curves.     

Monotonic subcritical crack growth in T42 high speed steel

R-curve behaviour in the microstructurally short crack regime has been reported mainly in ceramics, composites and polymers; this paper describes it for a metallic material: brittle cast and wrought T42 high speed steel. Continuum mechanics has demonstrated the general admissibility of sub-critical growth of cracks with a cohesive zone. Results now reported show that, in a metallic material, growth of microstructurally short cracks under monotonic loading, as in fatigue, is governed by microstructure (texture). Natural cracks, i.e. produced by the hot forging operation, or induced by the application of stress in the range 0.5 to 1.1 GPa in four-point bending experiments, of depths extending to 25μm were always associated with MC carbides. At comparable stress levels cracks were nucleated in compression -- surprisingly some transverse to the compressive axis. Observations of crack nucleation and subsequent studies of subcritical growth of these microcracks were made by surface replica microscopy. Crack extension was easy within the carbide stringers (a characteristic feature of hot-worked high speed steels), but, at higher stresses, took place between these bands to reach up to ∼ 100 μm (surface) length. Dormant cracks were shallow, no more than 6 μm deep; whereas those responsible for failure, at stresses ranging from 0.6 to 1.9 GPa, had a semicircular geomerty -- identified by scanning electron fractography. Step-wise monotonic subcritical crack growth is modelled asR -curves and it is shown that the maximum estimated (microscopic) applied stress intensity factor K _a can vary from 0.5 to 1.0 K_1C, the macroscopic fracture toughness independently determined using sharp artificial long cracks. This revised version was published online in August 2006 with corrections to the Cover Date.     

Analysis of vacuum fatigue crack growth results and its implications

Conventionally, the reduction of ΔK_th with load ratio R has been interpreted in terms of crack closure arising from plasticity, oxide or crack surface roughness. Since, plane-strain conditions exist near-threshold, plasticity-induced closure is absent. Therefore, to account for R-ratio effects near-threshold, the oxide and roughness closure mechanisms have been proposed. Further analysis has shown that these other two closure effects also are small, when the results taken in vacuum were included. The present analysis shows that there is a unique relation of the oxide thickness with a threshold K_max, rather than with a threshold ΔK. This threshold K_max (K*_max,th) depends on environment. When the applied K_max<K*_max,th, the crack is stationary in the presence of the oxide formation and grows only when the applied K_max>K*_max,th. Thus, the oxide thickness—K_max relation seems to have a bearing on the criterion for crack growth in the presence of the environment. Oxide formation passivates the crack surfaces and retards the environmental damage ahead of the crack-tip. Examples from CrMo and NiCrMo steels support this viewpoint and suggest that there is a pressing need for quantifying the crack-tip environmental effects and fatigue thresholds.     

A general expression for an area integral of a point-wise J for a curved crack front

The expression for the J-integral at a point on a three-dimensional crack front, obtained from a surface independent integral, is in general a sum of a contour integral and an area integral. In this work a general expression of an area integral for a crack with a curved front is derived in curvilinear coordinates. In certain situations the area integral vanishes and previously known cases are a straight crack front in plane stress or plane strain. The general conditions for a vanishing area integral are studied. It is shown that the area integral is non-zero for cracks with a curved front in the direction of crack extension. Some examples of curved cracks are given, for which the area integral vanishes and that are of interest in practice.     

Crack observation methods, their application and simulation of curved fatigue crack growth

The observation of cracks with curved crack path has to be done optically. It is shown that a modified commercial flat bed scanner and a combination of a high-resolution scanner camera system with 10,000 × 10,000 pixels with a telecentric lens are appropriate for high-resolution (up to 8 μm/pixel) optical recording of multiple crack ends on sample areas up to 210 mm × 290 mm. The high-resolution photographs are suitable for determination of crack lengths. It is also possible to observe crack paths or geometrical crack tip parameters and strain fields by image correlation. The method is used to determine static crack resistance and cyclic crack growth curves on center crack tension and biaxial cruciform samples.Furthermore, the paper presents an improved finite element technique for the simulation of curved fatigue crack growth in a multiple arbitrarily pre-cracked isotropic sheet under biaxial plane stress loading applying a predictor-corrector procedure in combination with the modified virtual crack closure integral (MVCCI) method including the consideration of the plastic limit loads. For this, the program PCCS-2D was extended to analyse the crack growth and the plastic limit load for each crack propagation step in a fully automatic simulation. The proposed solution algorithm provides a powerful tool for flaw assessment with the failure assessment diagram procedure in combination with a numerical crack path simulation. Finally, the simulation is verified experimentally.     

Temperature Dependence of Brittle Fracture Toughness of Reactor Pressure-Vessel Steels upon Ductile Crack Growth

The main mechanisms of brittle fracture upon ductile crack growth are studied on the basis of the probabilistic model of brittle fracture and the deterministic model of ductile fracture, which were put forward by the authors earlier. The investigations are carried out on the reactor pressure-vessel steel 15Kh2NMFAA in the initial and embrittled states. The dependences of brittle-fracture probability on the stress intensity factor and the value of ductile crack growth are calculated for various temperatures. The temperature dependence of brittle fracture toughness in the initial and embrittled states is predicted with and without regard for ductile crack growth. The authors analyze the main factors that govern the above-mentioned relationships. The calculated results are compared to test data for CT-type compact specimens.     

J-integral analysis of the interaction between an interface crack and parallel subinterface cracks in dissimilar anisotropic materials

The J-integral analysis is presented for the interaction problem between a macro-interface crack and subinterface microcracks parallel to the former in the near-tip process zone in dissimilar anisotropic composite materials. Elementary solutions respectively considering an interface crack and a subinterface crack subjected to different loads are given from which the interaction problem is deduced to a system of integral equations with the aid of superimposing technique (i.e., the so called `Pseudo-Traction Method' abbreviated as PTM). After the integral equations are solved numerically, a consistent relation among three kinds of the J-integral values is obtained. They are induced from the macro-interface crack tip, the microcracks, and the remote field, respectively. This consistent relation of the J-integral can be used to confirm the numerical results derived by using whatever kind of technique. With the aid of J-integral analysis, the interaction behaviors between an interface crack and parallel subinterface cracks are investigated in detail, and some special physical phenomena are obtained.     

A finite element analysis of stable crack growth in an aluminium alloy

Extensive stable cracking has been observed in large test pieces of 25 mm thick weldable AlMgZn alloy which is used in the construction of a portable bridge. Standard fracture specimens produced valid K_IC values, with short cracks exhibiting unstable fracture. Finite element analysis of the large specimens determined a valid J_R-curve that can increase the effective K_C by several times the K_IC value. The R-curve has an unusual ‘concave’ shape that is associated with the change from initially flat fracture to fully slant fracture. The early stages of the R-curve are affected by in-plane constraint that can be indexed by the T-stress. The R-curve can be used to explain the stability of long cracks in full-scale tests on a bridge prototype, compared with the instability of short cracks in small, standard test pieces.     

Effects of various environments on fatigue crack growth in Laser formed and IM Ti–6Al–4V alloys

The fatigue crack growth behaviors of Laser formed and ingot metallurgy (IM) Ti–6Al–4V alloys were studied in three environments: vacuum, air and 3.5% NaCl solution. Taking the Unified Fatigue Damage Approach, the fatigue crack growth data were analyzed with two intrinsic parameters, stress intensity amplitude ΔK and maximum stress intensity K_max, and their limiting values ΔK^* and . Fatigue crack growth rates da/dN were found increase with stress ratio R, highest in 3.5% NaCl solution, somewhat less in air and lowest in vacuum, and higher in IM alloy than in Laser formed one. In 3.5% NaCl solution, stress corrosion cracking (SCC) was superimposed on fatigue at R=0.9 for where K_max>K_ISCC, the threshold stress intensity for SCC. This and environment-assisted fatigue crack growth were evidenced by the deviation in fatigue crack growth trajectory (ΔK^* vs. curve) from the pure fatigue line where . Furthermore, the fractographic features, identified along the trajectory path, reflected the fatigue crack growth behaviors of both alloys in a given environment.     

Structural integrity of an X-750 jet pump beam of a BWR by means of FITNET FFS procedure

In this paper, the J–R curves of the X-750 alloy, previously obtained in the rising load test environment, have been implemented in the structural integrity assessment of a jet pump beam of a boiling water reactor manufactured in this material. The analysis was performed with the FITNET FFS procedure considering the in-service loads on the beam. The critical crack lengths for the different scenarios studied have been obtained and, taking into consideration real crack length velocities, the lifespan of the beams were conservatively estimated.     

Analyses of the fatigue crack propagation process and stress ratio effects using the two parameter method

In situ SEM observations (Zhang JZ. A shear band decohesion model for small fatigue crack growth in an ultra-fine grain aluminium alloy. Eng Fract Mech 2000;65:665–81; Zhang JZ, Meng ZX. Direct high resolution in-site SEM observations of very small fatigue crack growth in the ultra fine grain aluminium alloy IN 9052. Script Mater 2004;50:825–28; Halliday MD, Poole P, Bowen P. New perspective on slip band decohesion as unifying fracture event during fatigue crack growth in both small and long cracks. Mater Sci Technol 1999;15:382–90) have revealed that fatigue crack propagation in aluminium alloys is caused by the shear band decohesion around the crack tip. The formation and cracking of the shear band is mainly caused by the plasticity generated in the loading part of a load cycle. This shear band decohesion process has been observed to occur in a continuous way over the time period during the loading part of a cycle. Based on this observation, in this study, a new parameter has been introduced to describe fatigue crack propagation rate. This new parameter, da/dS, defines the fatigue crack propagation rate with the change of the applied stress at any moment of a stress cycle. The relationship between this new parameter and the conventional da/dN parameter which describes fatigue crack propagation rate per stress cycle is given.Using this new parameter, it is proven that two loading parameters are necessary in order to accurately describe fatigue crack propagation rate per stress cycle, da/dN. An analysis is performed and a general fatigue crack propagation model is developed. This model has the ability to describe the four general type of fatigue crack propagation behaviours summarised by Vasudevan and Sadananda (Vasudevan AK, Sadananda K. Fatigue crack growth in advanced materials. In: Fatigue 96, Proceedings of the sixth international conference on fatigue and fatigue threshold, vol. 1. Oxford: Pergamon Press; 1996. p. 473–8).     

Nucleation and growth of domains near crack tips in single crystal ferroelectrics

The nucleation and growth of domains is investigated near a stationary crack tip in a single crystal of ferroelectric material. The phase-field approach, applying the material polarization as the order parameter, is used as the theoretical modeling framework and the finite element method is used for the numerical solution technique. The electromechanical form of the J-integral is appropriately modified to account for the polarization gradient energy terms, and analyzed to illustrate the amount of shielding, or lack thereof, due to domain switching at the crack tip. It is shown that the nucleation of domains near the crack tip due to applied electric field is affected by applied stress. However, the crack-tip energy release rate can change significantly between the instant of domain nucleation and the final equilibrium domain configuration. Implications of these results for ferroelectric single crystal fracture criteria are discussed.     

Creep crack growth simulations in 316H stainless steel

Virtual methods of predicting creep crack growth (CCG), using finite element analysis (FE), are implemented in a compact tension specimen, C(T). The material examined is an austenitic type 316H stainless steel at 550 °C, which exhibits power-law creep–ductile behaviour. A local damage-based approach is used to predict crack propagation and the CCG rate data are correlated with the C^∗ parameter. Two-dimensional elastic–plastic–creep analyses are performed under plane stress and plane strain conditions. Finite element CCG rate predictions are compared to experimental data and to the NSW and modified NSW (NSW–MOD) CCG models’ solutions, which are based on ductility exhaustion arguments. An alternative version of the NSW–MOD model is presented for direct comparison with the FE implementation. The FE predictions are found to be in agreement with the appropriate analytical solutions, and follow the trends of the experimental data at high C^∗ values. Accelerated cracking behaviour is observed experimentally at low C^∗ values, which is consistent with the standard plane strain NSW–MOD prediction. The FE model may be developed to predict this accelerated cracking at low C^∗ values so that the trends between CCG rates at high and low C^∗ values may be determined.     

Crack growth in FeP04 steel under cyclic tension for different notches on the basis of its microstructure

We present the results of experimental work carried out in order to analyze the initiation and propagation of fatigue cracks in FeP04 steel. The tests were performed in plane specimens under cyclic tension by keeping constant the nominal load ratio R = 0. Crack paths on the basis of the tested material microstructure were observed. __________ Translated from Problemy Prochnosti, No. 1, pp. 121–124, January–February, 2008.     

Elastic–plastic analysis of interaction between an interfacial crack and a subinterfacial microcrack in bi-materials

In the present work the finite element method is used to analyze the effect of interaction between an interfacial crack and a microcrack in ceramic/aluminum bi-materials. The behaviour is analyzed by the determination of the J integral, the plastic zone at the tips of the interfacial crack and the microcrack. The effects of longitudinal and transversal distance between the tips of the two cracks and the rotation of the microcrack are examined. The obtained results allow us to deduce a correlation between the position of the microcrack and the J integral and the plastic zone.The obtained results shows that the J integral at the interfacial crack tip reaches a maximum value when the microcrack is moved in the vicinity of the interfacial crack. With this distance the effect of interaction is marked more; the stress field at the microcrack tip and that of the interfacial crack generates only one plastic zone at the interfacial crack tip. The maximum size of the plastic zone is localised at the interfacial crack tip. Those of the two tips of the microcrack are very weak and even negligible in front of the zone plasticized at the interfacial crack tip.     

Fractal modeling of the J-R curve and the influence of the rugged crack growth on the stable elastic-plastic fracture mechanics

In this paper, fractal geometry is used to modify the Griffith-Irwin-Orowan classical energy balance. Crack fractal geometry is introduced in the elastic-plastic fracture mechanics by means of the Eshelby-Rice J-integral and the influence of the ruggedness of the crack surface on the quasistatic crack growth is evaluated. It is shown that the rising of the J-R curve correlates to the topological ruggedness dimension of the crack surface. Results from fracture experiments are shown to be very well fitted with the proposed model, which is shown to be a unifying approach for fractal models currently used in fracture mechanics.     

Determination of double-Determination of double-K criterion for crack propagation in quasi-brittle fracture Part I: experimental investigation of crack propagation

The results of experimental investigations using laser speckle interferometry on small size three-point bending notched beams and using photoelastic coating and the strain gauges on very large size compact tension specimens of concrete are presented in detail. The investigations showed that there exists a stage of stable crack propagation before unstable fracture occurs. The results are in agreement with other researchers' investigations using moire interferometry, holographic interferometry, dye-impregnation method and microscope. Further detailed study shows that the three different states, i.e., crack initiation, stable crack propagation and unstable fracture can be distinguished in the fracture process in concrete structures. In order to predict the crack propagation during the fracture process in quasi-brittle materials a double-K criterion is proposed. The double-K criterion consists of two size-independent parameters. Both of them are expressed in terms of the stress intensity factors. One of them reflects the initial cracking toughness, denoted with Kⁱⁿⁱ, which can be directly evaluated by the initial cracking load, P_ini, and the precast crack length, a₀, using a formula of LEFM. The other one refers to the unstable fracture toughness, denoted with K^un, which can be obtained inserting the maximum load, P_max, and the effective crack length, a, into the same formula of LEFM. The values of the two parameters, K _Ic ⁱⁿⁱ and K _Ic ^un , obtained from the small size three-point bending notched beams and the large size compact tension specimens show that K _Ic ⁱⁿⁱ and K _Ic ^un are size-independent. Evaluating with the K-resistance curves obtained from the same test data, it is found that the proposed double-K criterion is equivalent to it in basic principle, but, the double-K criterion can be applied more easily than the K-resistance curve. Finally, as a practical example, the application of the double-K criterion to the prediction of the crack propagation in a concrete dam is discussed.