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.     

MIXED-MODE FRACTURE MECHANISMS NEAR THE FATIGUE THRESHOLD OF AISI 316 STAINLESS STEEL

Abstract— Near threshold, mixed mode (I and II), fatigue crack growth occurs mainly by two mechanisms, coplanar (or shear) mode and branch (or tensile) mode. For a constant ratio of ΔK_I/ΔK_II the shear mode growth shows a self-arrest character and it would only start again when ΔK_I and ΔK_II are increased. Both shear crack growth and the early stages of tensile crack growth, are of a crystallographic nature; the fatigue crack proceeds along slip planes or grain boundaries. The appearance of the fracture surfaces suggest that the mechanism of crack extension is by developing slip band microcracks which join up to form a macrocrack. This process is thought to be assisted by the nature of the plastic deformation within the reversed plastic zone where high back stresses are set up by dislocation pile-ups against grain boundaries. The interaction of the crack tip stress field with that of the dislocation pile-ups leads to the formation of slip band microcracks and subsequent crack extension. The change from shear mode to tensile mode growth probably occurs when the maximum tensile stress and the microcrack density in the maximum tensile plane direction attain critical values.     

Elastic interaction of a crack with a random array of microcracks

Two issues are addressed in the paper. The first deals with a new characterization of a random array of microcracks in terms of spatial distributions of the sizes, orientations and density of microcracks. The second is a formulation of crack-microcrack array interaction in terms of the distributions. The interaction problem is posed as a system of two coupled singular integral equations with respect to a vector field of an average microcrack opening and the main crack opening displacement. The approach is illustrated by a numerical solution of the interaction problem for two particular configurations of a random array of microcracks. It is shown that the morphology of the microcrack array may strongly alter elastic fields in the vicinity of the main crack. Specifically, it is found that a variation in the microcrack length distribution (for fixed distributions of microcrack orientation and density) has a profound effect on the solution. The main crack opening displacement is evaluated to compare the theory with the experimental observations.     

Micro-mechanical analysis and TEM study of crack initiation in dislocation free zone

Dislocation emission, dislocation-free zone (DFZ) formation and crack initiation in the DFZ and/or at the crack tip were analyzed by micromechanics. The results show that a DFZ is formed after dislocation emission under constant load. The DFZ size decreases with increase in the applied stress intensity factor K _Ia or lattice friction stress _f. There are two stress peaks ahead of the crack tip. The first one is located at the blunt crack tip and the second one in the DFZ. With increasing in the applied stress intensity factor K _Ia, the peak stress at the crack tip may decrease while the peak stress in the DFZ increases monotonically. Microcrack will initiate when the peak stress is equal to the cohesive strength. In situ tensile tests in a transmission electron microscope (TEM) show that microcrack initiates in DFZ or/and at a blunt crack tip after dislocation emitting and DFZ formation.     

Stress field interaction and strain energy distribution between a stationary main crack and its process zone

The damage process zone developed by brittle materials in front of a macrocrack is simulated by means of a distribution of microcracks. Crack mutual interactions are taken into account by means of a numerical technique, based on a displacement discontinuity boundary element method that is able of considering both the macrocrack–microcrack and microcrack–microcrack interactions inside the process zone. In the frame of linear elastic fracture mechanics the stress field at each crack tip and the related elastic strain energy are calculated. The main features of the interaction phenomena turn out to be almost independent of the microcrack density. Some considerations both on the shielding and amplification effects on the main crack and on the strain energy distribution between cracks give explanation to experimental evidence and prove that crack interaction is not such a short-range effect as sometimes expected.     

Interaction effect of a main crack emanating from a semicircular notch and a microcrack

The study of morphology of fracture surfaces cannot only answer the whole of the problems arising from the damage of microcracking. This damage generates energy dissipation and a stress field redistribution which contributes to the dissipation of the energy stored in the structure, and favours the stable propagation of the main crack. In this work, the finite element method is used to analyze the interaction effect of a main crack emanating from semicircular notch and a microcrack in order to understand the different mechanisms induced by this interaction and in particular the effects of reduction and/or amplification of the stress field between the macro and the microcrack. Two cases were considered: transverse and longitudinal displacement of the microcrack compared to the main crack. This kind of approach makes it possible to predict the predominating fracture mode, either by coalescence, or by deflection in the direction of mode II.     

Near-tip microcrack shielding in advanced ceramics

Recent manufacturing of advanced ceramics has developed phase transformation and cracks tilted or bridged to enhance ceramic‐inherent toughness. However, main crack and near‐tip microcracks interaction is another prominent means in toughening of the ceramic materials. In this study, mechanics of discrete model combined with alternative iterating numerical technique is developed and applied in assessment of main–microcrack interaction. Consequences of main–microcrack interaction can either shield or amplify the resulting main crack stress intensity factor, which accounts for the increase or decrease of ceramic toughness. Numerical outcomes show good agreement with the available solutions in the literatures; in addition results also reveal that the toughness shielding or amplification is dependent on the type of loadings as well as location/orientation of the microcrack. Nevertheless, residual normal stress plays an important role in shielding/amplification region trade‐off. This work may provide a useful quantitative tool in ceramic design and a valuable insight into main–micro interaction phenomenon.     

A fracture mechanics model for the analysis of micro-pitting in regard to lubricated rolling–sliding contact problems

A computational model is presented for the analysis of micro-pitting in regard to lubricated rolling–sliding contact problems. This model assumes the appearance of an initial microcrack on the contact surface due to the mechanical or thermal treatment of the material, and as a consequence of an on-going process in early the stage of exploitation. The discretised model of the contacting mechanical elements is subjected to normal loading (Hertzian contact pressure), tangential loading (friction between contacting surfaces) and internal pressure to the crack surfaces. Crack propagation is predicted as follows: (1) using modified maximum tangential stress criterion, which takes into account the influence of stress intensity factors K_I and K_II, T-stress, stress on the crack’s surface caused by lubricant pressure inside the crack, and the critical distance ahead of the crack tip and (2) the classical maximum tangential stress criterion, which only takes into account the influence of the stress intensity factors K_I and K_II. The stress intensity factor based on these two criteria is then used in a short crack growth theory to determine the fatigue life of an initial crack to extent up to micro-pit. The developed model is applied to a real spur gear pair.     

Some contribution to process zone fracture mechanics

The mechanism of the ductile fracture is studied theoretically for the Al Alloy 7075-T6 specimens. A model for the interaction of a crack tip with a void nearby is analyzed by using the Modified Gurson's Model. Taking fracture criterion into consideration, the analysis of a crack propagation is carried out and besides the distribution of the equivalent plastic strain, the void volume fraction f and the localization are obtained. Microcracks nucleate on the ligament between crack and void, and grow and coalesce each other, and at last the main crack thus formed coalesces with the void and the coalescence of the crack and void is completed. And these phenomenon occurs in the localized region.The initiation of the microcrack of 7075 occurs at small J and the microcrack penetration between crack and void occurs at larger J, and the propagation does not occur smoothly. These results coincide with the results of the experiments by FRASTA (FRActure Surface Topographic Analysis) and Fractography.     

Interaction effect crack–interfacial crack using finite element method

The interaction effect of an interfacial crack–microcrack modifies considerably the fracture behaviour of S45C/Si₃N₄ bimaterial. This work aims at studying the interaction effect of a crack located in one of the materials constituting the assembly near the interface, and that between an interfacial crack and a microcrack parallel to the interface by using the finite element method. The effect of transverse and longitudinal interaction distances between the interfacial crack and the microcrack are highlighted. The stress intensity factor of the interacting cracks and the bimaterial mechanical properties influence on the conditions of deviation and propagation of crack by interface and intercrack are examined.     

Estimating stress intensity factors with singular components of the total finite element solution

Displacement formulated singular elements are compared to isoparametric quarter-node elements. The total stress and displacement solution for each element is decomposed into singular and regular components for evaluating stress intensity factors. Specific relationships between nodal displacements and the singular component of stress are presented for the isoparametric element at selected locations within the element. Numerical results for K_I and K_II in the slant crack problem are presented. The singular components are shown to produce superior results when considering crack opening displacements.     

Stress intensity factor solutions for a cracked bolt loaded by a nut

This paper presents the calculation of stress intensity factor (K) solutions for surface cracks in the thread ground of bolts subjected to axial loading directly applied by the nut. The stress-strain computations have been done by means of the finite element method with quarter-point singular isoparametric elements along the crack front. The stress intensity factor is calculated through the stiffness derivative method, by using a virtual crack extension technique to compute the energy release rate. Two modifications are made to improve the accuracy of the results: the displacement not only of the main node, but also of the quarter-point nodes located in the normal plane and the adjacent nodes in the crack line, avoiding both the change of the singularity and the crack curving. The results show that direct loading on the thread flank by a nut increases the stress intensity factor. This effect decreases with the crack length. For the deepest circular cracks, however, nut loading relaxes the K-value, mainly at the crack surface.     

A global collocation technique for the solution of opening mode crack problems

A review of various experimental and numerical techniques for determination of fracture mechanics calibration functions (i.e., the variation of K ₁ and CMOD with crack length) revealed that neither technique, employed independently, can determine K ₁, CMOD, and full field stresses in closed form over a wide range of crack lengths. To fill this void, a combined experimental/numerical collocation technique based on a series expansion of the modified Westergaard functions was developed. This technique uses both boundary conditions, known a priori, and interior stress field conditions, determined using a suitable experimental technique, for analysis of two dimensional, finite body, opening mode crack problems. This paper reports on an investigation of the accuracy of this technique and its sensitivity to errors in experimental data for a sample problem of practical interest.     

Interactions of a sub-surface crack with a center of dilatation in an elastic half-plane

This paper examines the interaction between a crack parallel to the free surface of an elastic half-plane and an internal center of dilatation. The problem is decomposed into two auxiliary problems. When the center of dilatation approaches the crack tip, two kinds of singularity are analytically obtained. If the overburden stress and the friction on crack surface are neglected, both modes I and II stress intensity factors (K_I and K_II) are induced at the crack tips. The maximum of K_I and K_II occurs when the center of dilatation is located in front of the crack tips. The tensile cracking is likely to be prohibited by the overburden stress, while shear cracking remains possible even including the effects of both overburden and friction on the crack surface.     

Mechanisms for corrosion fatigue crack propagation

ABSTRACT The corrosion fatigue crack growth (FCG) behaviour, the effect of applied potential on corrosion FCG rates, and the fracture surfaces were studied for high‐strength low‐alloy steels, titanium alloys, and magnesium alloys. During investigation of the effect of applied potential on corrosion FCG rates, polarization was switched on for a time period in which it was possible to register the change in the crack growth rate corresponding to the open‐circuit potential and to measure the crack growth rate under polarization. Due to the higher resolution of the crack extension measurement technique, the time rarely exceeded 300 s. This approach made possible the observation of a non‐single mode effect of cathodic polarization on corrosion FCG rates. Cathodic polarization accelerated crack growth when the maximum stress intensity (K_max) exceeded a certain well‐defined critical value characteristic for a given material‐solution combination. When K_max was lower than the critical value, the same cathodic polarization, with all other conditions (specimen, solution, pH, loading frequency, stress ratio, temperature, etc.) being equal, retarded or had no influence on crack growth. The results and fractographic observations suggested that the acceleration in crack growth under cathodic polarization was due to hydrogen‐induced cracking (HIC). Therefore, critical values of K_max, as well as the stress intensity range (ΔK) were regarded as corresponding to the onset of corrosion FCG according to the HIC mechanism and designated as K_HIC and ΔK_HIC. HIC was the main mechanism of corrosion FCG at K_max > K_HIC (ΔK > ΔK_HIC). For most of the material‐solution combinations investigated, stress‐assisted dissolution played a dominant role in the corrosion fatigue crack propagation at K_max < K_HIC (ΔK < ΔK_HIC).     

Empirical model for plasticity‐induced crack closure based on Kmax and ΔK

The mean stress has a significant effect on crack propagation life and must be included in prediction models. However, there is no consensus in the fatigue community regarding the dominant mechanism explaining the mean stress effect. The concept of crack closure has been widely used and several empirical models can be found in literature. The stress ratio, R, is usually the main parameter of these models, but present numerical results showed a significant influence of K_max. A new empirical model is therefore proposed here, dependent on K_max and ΔK, with four empirical constants. The model also includes the effect of material's yield stress, and two additional parameters were defined to account for stress state and crack closure parameter. A comparison was made with Kujawski's and Glinka's parameters, for a wide range of loading conditions. ΔK_eff lies between Kujawski's and Glinka's parameters, and some agreement is evident, although the concepts are quite different. The crack opening model was applied to literature results and was able to collapse da/dN–ΔK curves for different stress ratios to a single master curve.     

A MICROCRACK GROWTH LAW FOR MULTIAXIAL FATIGUE

Within the past decade, critical plane approaches have gained increasing support based on correlation of experimentally observed fatigue lives and microcrack orientations under predominately low cycle fatigue (LCF) conditions for various stress states. In this paper, we further develop an engineering model for microcrack propagation consistent with critical plane concepts for correlation of both LCF and high cycle fatigue (HCF) behavior, including multiple regimes of small crack growth. The critical plane microcrack propagation approach of McDowell and Berard serves as a starting point to incorporate multiple regimes of crack nucleation, shear growth under the influence of microstructural barriers, and transition to linear crack length-dependent growth related to elastic-plastic fracture mechanics (EPFM) concepts. Microcrack iso-length data from uniaxial and torsional fatigue tests of 1045 steel and IN 718 are examined and correlated by introducing a transition crack length which governs the shift from nonlinear to linear crack length dependence of da/dN. This transition is related to the shift from strong microstructural influence to weak influence on the propagation of microcracks. Simple forms are introduced for both the transition crack length and the crack length-dependence of crack growth rate within the microcrack propagation framework (introduced previously by McDowell and Berard) and are employed to fit the 1045 steel and IN 718 microcrack iso-length data, assuming preexisting sub-grain size cracks. The nonlinear evolution of crack length with normalized cycles is then predicted over a range of stress amplitudes in uniaxial and torsional fatigue. The microcrack growth law is shown to have potential to correlate microcrack propagation behavior as well as damage accumulation for HCF-LCF loading sequences and sequences of applied stress states.     

The interaction of multiple rows of periodical cracks

In this paper, the interaction of multiple rows of periodical cracks contained in an infinite elastic plate with far-field stress loaded is studied. An extremely accurate and efficient numerical method for solving the problem is presented. The method is mainly by means of the crack isolating analysis technique, stress superposition principle, the Chebyshev polynomial expansion of the pseudo-traction as well as the segmental average collocation technique. This method can be used to compute the stress intensity factors of multiple cracks, periodical cracks, and multiple rows of periodical cracks. In the process of dealing with the superposition of interaction of infinite number of periodic cracks, a key series summation technique is used, which aims at numerical results with extremely high accuracy but with less computation work. Many complex computing examples are given in this paper, and, for some typical examples, numerical results are compared with analytic solutions and with previous numerical solutions. For the problem of the one periodical collinear cracks, the accuracy given by this method reaches to 6 significant digits if a/d 0.9 (where a is the half crack length, and d is the half crack spacing). And even if a/d=0.99, the error is still less than 0.5%. The computer results for multiple rows of periodic collinear and echelon cracks show that the interaction effect between two rows rapidly decline with exponential law as the array pitch increases. This method has filled the gaps in the research field on the interaction of multiple rows of general periodical cracks.     

Evaluation of overload effects on fatigue crack growth and closure

Fatigue crack propagation tests with single tensile peak overloads have been performed in 6082-T6 aluminium alloy at several baseline ΔK levels and stress ratios of 0.05 and 0.25. The tests were carried out at constant ΔK conditions. Crack closure was monitored in all tests by the compliance technique using a pin microgauge. The observed transient post-overload behaviour is discussed in terms of overload ratio, baseline ΔK level and stress ratio. The crack closure parameter U was obtained and compared with the crack growth transients. Experimental support is given for the hypothesis that plasticity-induced closure is the main cause of overload retardation for plane stress conditions. Predictions based on crack closure measurements show good correlation with the observed crack growth rates for all the post-overload transients when discontinuous closure is properly taken into account.