On the contribution of a microhole in the near-tip stress field to the J-integral

The J-integral analysis is performed for the interaction of a macrocrack with a microhole in a homogeneous plane of a linear elastic solid. A simple relation is obtained between three kinds of the J-integral induced by the macrocrack tip, the microhole and the remote stress field, respectively. The anti-shielding effect or the shielding effect of the microhole on the macrocrack can be confined easily from the J-integral induced from the microhole. This revised version was published online in August 2006 with corrections to the Cover Date.     

Crack shielding and amplification due to multiple microcracks interacting with a macrocrack

Abatract We investigate the effect of crack shielding and amplification of various arrangements of microcracks on the stress intensity factors of a macrocrack, including large numbers of arbitrarily aligned microcracks. The extended finite element method is used for these studies. In some cases the numerical XFEM simulation provides results that are more accurate than currently available analytical approximations because the assumptions are less restrictive than those made in obtaining analytical approximations. Stress intensity factors for the tip of a macrocrack under the influence of nearby microcracks are calculated under far field mode 1 boundary conditions. For a microcrack aligned with the macrocrack the numerical results agree quite well with the analytically exact stress intensity factors. The influence of the distance to the macrocrack tip and the rotation angle is investigated for unaligned microcracks, and it is shown in several examples with many randomly distributed microcracks that the influence of those microcracks which are not in close proximity to the macrocrack tip is on the order of 5%.     

The effect of an elliptical hole on the stress intensity factor of a macrocrack

The effect of an elliptical hole on the stress intensity factor of a semi-infinite crack (macrocrack) under Mode III loading condition is considered. Numerical results reveal that the shape of the microdefect has pronounced influence on the stress intensity factor of the macrocrack, especially when the tip-to-centre distance becomes small.     

Analysis of micro--macro material properties and mechanical effects of damaged material containing periodically distributed elliptical microcracks

The existence of numerous microcracks causes changes in the stiffness or fracture toughness of materials. In this paper, the manifestations of mechanical properties in the damaged materials caused by the microcracks are evaluated by the present homogenization method based on the superposition method together with the VNA solution. Moreover, it is known that the stress concentration at the macrocrack tip decreases due to the stress relaxation effect caused by the existence of the microcracks. In order to evaluate the manifestations of mechanical behavior, the mechanical effects of the existence of the microcracks on the macrocrack, the component separation method for mixed-mode stress intensity factors of the macrocrack in the damaged materials is newly developed in this paper. Various numerical analyses are successfully conducted for the two topics, the mechanical properties of the damaged materials and the mechanical behavior of the macrocrack in the damaged materials.     

Plane problem of macro-microcrack interaction taking account of crack closure

The fracture stability of a macrocrack under the tensile and shear loading in the presence of a system of microcracks is analysed. Interaction of cracks leads to full or partial closure of the crack edges. The boundary problem is formulated and a solution is obtained by the small parameter method. Domains where microcracks are closed, and regions where microcracks cause full or partial closure of the macrocrack are found. The influence of crack contact on the stress intensity coefficient is analysed under the friction free assumption.     

Modeling the brittle–ductile transition in ferritic steels: dislocation simulations

We present a model for the brittle–ductile transition in ferritic steels based on two dimensional discrete dislocation simulations of crack-tip plasticity. The sum of elastic fields of the crack and the emitted dislocations defines an elasto–plastic crack field. Effects of crack-tip blunting of the macrocrack are included in the simulations. The plastic zone characteristics are found to be in agreement with continuum models, with the added advantage that the hardening behavior comes out naturally in our model. The present model is composed of a macrocrack with microcracks ahead of it in its crack-plane. These microcracks represent potential fracture sites at internal inhomogeneities, such as brittle precipitates. Dislocations that are emitted from the crack-tip account for plasticity. When the tensile stress along the crack plane attains a critical value σ _F over a distance fracture is assumed to take place. The brittle–ductile transition curve is obtained by determining the fracture toughness at various temperatures. Factors that contribute to the sharp upturn in fracture toughness with increasing temperature are found to be: the increase in dislocations mobility, and the decrease in tensile stress ahead of the macrocrack tip due to increase in blunting, and the slight increase in fracture stress of microcracks due to increase in plasticity at the microcrack. The model not only predicts the sharp increase in fracture toughness near the brittle–ductile transition temperature but also predicts the limiting temperature above which valid fracture toughness values cannot be estimated; which should correspond to the ductile regime. The obtained results are in reasonable agreement when compared with the existing experimental data.     

Prediction of the Durability of Cyclically Loaded Structural Elements

A procedure of determination of the durability of cyclically loaded notched specimens is proposed and experimentally verified. The procedure is based on the concepts of the unified model of fatigue fracture treating the processes of initiation and propagation of a fatigue macrocrack from the common point of view. For specimens with structural stress concentrators of two types, we compute the periods of initiation and growth of a fatigue macrocrack and the number of loading cycles to failure on the basis of the diagrams of fatigue crack growth rates. The numerical results agree with the experimental data with an error of at most 38% depending on the method of calculations and durability. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 4, pp. 39–44, July–August, 2005.     

Application of the method of acoustic emission to the evaluation of the influence of mechanical cycling on the kinetics of fracture and the crack-growth resistance of A3 structural steel

We determine the parameters of acoustic emission that characterize different stages of the process of accumulation of damage, including the onset of the process of coalescence of pores and the initiation and growth of a macrocrack. It is shown that the process of initiation of a tensile macrocrack depends on the size of the stress concentrator, i.e., on the type of stressed state, to a greater extent than on the number of cycles of mechanical loading.     

A Probabilistic Method to Predict Fatigue Crack Initiation

A probabilistic method to predict macrocrack initiation due to fatigue damage is presented in this paper. Acoustic non-linearity is used to quantify pre-macrocrack initiation damage. This data is then used in a probabilistic analysis of fatigue damage. The probabilistic fatigue damage analysis consists of a suitably chosen damage evolution equation to model accumulated damage coupled with a procedure to calculate the probability of macrocrack initiation. The probability of macrocrack initiation is evaluated using the Monte Carlo Method with Importance Sampling. Numerical results for the probabilistic assessment of fatigue damage for a sample problem are presented and compared with experimental results.     

Application of the method of acoustic emission to the evaluation of the influence of mechanical cycling on the kinetics of fracture and the crack-growth resistance of A3 structural steel

We determine the parameters of acoustic emission that characterize different stages of the process of accumulation of damage, including the onset of the process of coalescence of pores and the initiation and growth of a macrocrack. It is shown that the process of initiation of a tensile macrocrack depends on the size of the stress concentrator, i.e., on the type of stressed state, to a greater extent than on the number of cycles of mechanical loading. Translated from Problemy Prochnosti, No. 6, pp. 126–130, November–December, 1997.     

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.     

Fracture mechanisms near threshold conditions of nickel alloyed PM steel

The paper examined fractographically four nickel alloyed powder metallurgy (PM) steels with total porosity between 3 and 9%. Fracture surfaces were inspected on smooth rectangular specimens from constant stress amplitude tests under axial loading with zero mean stress, at 30 Hz frequency.

The area containing the fatigue crack origin was observed in a region located invariably at a specimen surface. In all cases, the fracture surface was composed of three different morphological appearances (regions) associated with changed proportions of particular fracture mechanisms: macrocrack initiation region where cracks propagated preferentially through particles and there was no influence of pores on the propagation paths; in the other regions (macrocrack growth and unstable crack growth) cracks propagated mainly through the sintering necks by ductile rupture from microvoid coalescence and transparticle cleavage fracture.     

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.     

Time-domain boundary element analysis of dynamic near-tip fields for impact-loaded collinear cracks

A time-domain boundary integral equation method has been developed to calculate elastodynamic fields generated by the incidence of stress (or displacement) pulses on single cracks and systems of two collinear cracks. The system of boundary integral equations has been cast in a form which is amenable to solution by the boundary element method in conjunction with a time-stepping technique. Particular attention has been devoted to dynamic overshoots of the stress intensity factors. Elastodynamic stress intensity factors for pulse incidence on a single crack have been computed as function of time, and they have been compared with results of other authors. For collinear macrocrack-microcrack configurations the stress intensity factors at both tips of the macrocrack have been computed as functions of time for various values of the crack spacing and the relative size of the microcrack.     

Stress-strain state of specimens used to investigate the initiation and growth of cracks

The stress-strain state of a rectangular plate with a central circular hole and a disk with an edge notch is examined in both the elastic and elastoplastic statement. The stress intensity factors at the tips of cracks emerging from the hole and notch are determined. Parameters describing the process of crack initiation and development are established in the zone of the stress risers. The results of calculations are compared with experimental data in evaluating the period of macrocrack initiation.Translated from Problemy Prochnosti, No. 10, pp. 9–17, October, 1991.The authors express sincere thanks to Candidate of Technical Sciences A. I. Zboromirskii, who participated in the acquisition of analytical results of the study.     

On the relationship between fatigue limit,threshold and microstructure of a low-carbon Cr-Ni steel

The relationship between the fatigue limit stress range, Δσ_w, the threshold stress intensity factor, ΔK_th, and microstructure of low-carbon 12CrNi3A steel has been investigated. Non-propagating microcracks were observed on the surface of smooth specimens which has been subjected to at least 5 × 10⁶ cycles at the fatigue limit stress. The size of the cracks depended on the characteristic sizes of the microstructure of the material. Scanning electron microscopy showed that the fractographic characteristics in the near-threshold region of fatigue macrocrack growth were similar to those in the fatigue microcrack initiation region. This implies that the fatigue limit and fatigue threshold of the material have a similar physical meaning, both signifying the resistance of the material to the propagation of fatigue cracks. The relationship ΔK_th = 1.12Δσ_W √πα was shown to be valid, where a is a material parameter relating to microstructure, rather than to the length of a macrocrack. The results also showed that the value of a depends on the material and microstructure, and that both Δσ_W and ΔK_th will change if the microstructural characteristics of the material change.     

A phenomenological model of fatigue macrocrack initiation near stress concentrators

Fatigue macrocrack initiation is considered to be a two-parameter process. It is governed by the local or strain amplitude, and a certain linear parameter of the material. Corresponding parameters have been proposed, i.e. the local stress range Δσ*y and a characteristic distance d *, the prefracture zone size. The formation of this zone is conditioned by a decrease in yield strength within the material’s surface layers, microstructure, loading amplitude, cyclic strain hardening and environment. The value of d * is estimated experimentally by several methods and is assumed to be a certain material constant, independent of both notch and specimen geometry. At the prefracture zone boundary, a major barrier exists that retards the growth of a physically small fatigue crack. The moment when the physically small crack overcomes the prefracture zone boundary is assumed to be a quantitative criterion, a_{i = d *}, for the micro- to macrocrack transition. The proposed relationships, Δσ*y versus N_i , and d * versus N_i , can be used as a basis for the establishment of the materials resistance to macrocrack initiation.     

Investigation of macrocrack-microcrack interaction problems in anisotropic elastic solids – Part I: General solution to the problem and application of the J-integral

A general solution is derived for the plane problem of multiple microcracks near the tip in process zone of a semi-infinite macrocrack in an anisotropic elastic solid. The pseudo-traction method, addressed thoroughly in isotropic cases, is extended to anisotropic cases. A system of Fredholm integral equations, with difficulty in evaluation of the singular integrals, is solved by invoking the asymptotic behavior of the pseudo-tractions on the macrocrack faces. The interaction effect of the release of residual stresses due to near-tip microcracking is then evaluated. The J-integral analysis is also performed to give a consistency check of the solution and some useful conclusions. This revised version was published online in July 2006 with corrections to the Cover Date.     

T-effect for the interaction problem of an interface macrocrack with a near-tip microvoid

The paper deals with the analysis of the T-effect in the problem of an interface macrocrack interacting with a microvoid in the process zone of the main crack tip. With the aid of the `pseudo-traction-edge-dislocation' method, the interaction problem with the T-effect under the remote field loading conditions can be reduced to singular Fredholm integral equations with Hilbert kernel. After solving the singular integral equations numerically, the T-effect on the main crack tip parameters is analyzed and the numerical results are given in figures.     

Calculating the cracking resistance of ceramics by a numerical experiment method

Various mechanisms of main crack propagation in a polycrystalline material are examined on the basis of a previously proposed numerical model of the microstructure. Intergranular macrocrack growth in the presence of microcracks in part of intercluster boundaries is examined in the plane case, whereas the mixed failure including intergranular or transgranular propagation of the macrocrack in relation to the cracking resistance value is examined in the spatial case. The effect of elements of the microstructure (microcracks and voids) on the strength characteristics of the material is determined.Translated from Problemy Prochnosti, No. 7, pp. 34–37, July, 1991.