Crack propagation from a pre-existing flaw at a notch root – II: Detailed form of the stress intensity factors at the initial crack tip and conclusion.

This paper pursues the study of crack kinking from a pre-existing crack emanating from some notch root. It was shown in Part I that the stress intensity factors at the tip of the small initial crack are given by universal (that is, applicable in all situations, whatever the geometry of the body and the loading) formulae; they depend only on the `stress intensity factor of the notch' (the multiplicative coefficient of the singular stress field near the apex of the notch in the absence of the crack), the length of the crack, the aperture angle of the notch and the angle between its bisecting line and the direction of the crack. Here we identify the universal functions of the two angles just mentioned which appear in these formulae, by considering the model problem of an infinite body endowed with a notch with straight boundaries and a straight crack of unit length. The treatment uses Muskhelishvili's complex potentials formalism combined with some conformal mapping. The solution is expressed in the form of an infinite series involving an integral operator, which is evaluated numerically. Application of Goldstein and Salganik's principle of local symmetry then leads to prediction of the kink angle of the crack extension. It is found that although the direction of the crack is closer to that of the bisecting line of the notch after kinking than before it, the kink angle is not large enough for the crack tip to get closer to this line after kinking, except perhaps in some special situations.     

Fatigue crack initiation at notches in SA 333 piping steel

Abstract

In this paper are reported two recent investigations into crack initiation at notch roots using techniques developed for remote monitoring of crack growth in high–temperature water environments. In the first, a notched compact–type specimen of a carbon steel, SA 333 Gr. 6, was monitored for crack initiation (defined as a 0·076 mm crack at the notch root) in a variety of water chemistries and testing conditions. The mechanical conditions at the notch root have been analysed using the Neuber–notch method, enabling a direct comparison to be made with the strain–controlled fatigue data curves used for a smooth specimen in the ASME Boiler and Pressure Vessel Code, Section III. In the second investigation a different method was considered for monitoring crack initiation. A modification of the electrical–potential technique, called the reversing dc electrical potential method, was used to obtain quantitative information on the initiation and early growth of small surface cracks in notched bars of a high–strength alloy at elevated temperature. Results obtained by the method are presented and discussed.

MST/72     

EIFS-based crack growth fatigue life prediction of pitting-corroded test specimens

Corrosive environment causes corrosion pits at material surface and reduces the fatigue strength significantly. Fatigue crack usually initiates at and propagates from these locations. In this paper, a general methodology for fatigue life prediction for corroded specimens is proposed. The proposed methodology combines an asymptotic stress intensity factor solution and a power law corrosion pit growth function for fatigue life prediction of corroded specimens. First, a previously developed asymptotic interpolation method is proposed to calculate the stress intensity factor (SIF) for the crack at notch roots. Next, a growing semi-circular notch is assumed to exist on the specimen’s surface under corrosive environments. The notch growth rate is different under different corrosion conditions and is assumed to be a power function. Fatigue life can be predicted using the crack growth analysis assuming a crack propagating from the notch root. Plasticity correction is included into the proposed methodology for medium-to-low cycle fatigue analysis. The proposed methodology is validated using experimental fatigue life testing data of aluminum alloys and steels. Very good agreement is observed between experimental observations and model predictions.     

Rectangular Tensile Sheet with Double Edge Notch Cracks

This paper deals with the rectangular tensile sheet with symmetric double edge notch cracks. Such a crack problem is called an edge notch crack problem for short. By using a hybrid displacement discontinuity method (a boundary element method), two edge notch models are analyzed in detail. By changing the geometrical forms and parameters of the edge notch, and by comparing the stress intensity factors (SIFs) of the edge notch crack problem with those of the double edge cracked plate tension specimen (DECT), which is a model frequently used in fracture mechanics, the effect of the geometrical forms and parameters of the edge notch on the SIFs of the DECT specimen, is revealed. Some geometric characterestic parameters are introduced here, which are used to formulate the notch length and the branch crack length, which are to be determined in mechanical machining of the DECT specimen So we can say that the geometric characterestic parameters and the formulae used to determine the notch length and the branch crack length presented in this paper perhaps have some guidance role for mechanical machining of the DECT specimen.     

Crack growth resistance behavior of a functionally graded material: computational studies

This paper describes crack growth resistance simulation in a ceramic/metal functionally graded material (FGM) using a cohesive zone ahead of the crack front. The plasticity in the background (bulk) material follows J₂ flow theory with the flow properties determined by a volume fraction based, elastic-plastic model (extension of the original Tamura-Tomota-Ozawa model). A phenomenological, cohesive zone model with six material-dependent parameters (the cohesive energy densities and the peak cohesive tractions of the ceramic and metal phases, respectively, and two cohesive gradation parameters) describes the constitutive response of the cohesive zone. Crack growth occurs when the complete separation of the cohesive surfaces takes place. The crack growth resistance of the FGM is characterized by a rising J-integral with crack extension (averaged over the specimen thickness) computed using a domain integral (DI) formulation. The 3-D analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates solid elements with graded elastic and plastic properties and interface-cohesive elements coupled with the functionally graded cohesive zone model. The paper describes applications of the cohesive zone model and the DI method to compute the J resistance curves for both single-edge notch bend, SE(B), and single-edge notch tension, SE(T), specimens having properties of a TiB/Ti FGM. The numerical results show that the TiB/Ti FGM exhibits significant crack growth resistance behavior when the crack grows from the ceramic-rich region into the metal-rich region. Under these conditions, the J-integral is generally higher than the cohesive energy density at the crack tip even when the background material response remains linearly elastic, which contrasts with the case for homogeneous materials wherein the J-integral equals the cohesive energy density for a quasi-statically growing crack.     

Notch fatigue behaviour of low-temperature gaseous carburised 316L austenitic stainless steel

ABSTRACT

The influence of low-temperature gaseous carburisation on notch fatigue behaviour of 316L steel under cyclic axial loading was investigated. After carburisation, the carburised case was well distributed at the surface region and was not influenced by the notch geometry. Low-temperature carburisation considerably enhanced the notch fatigue performance, which led to 32% and 44% increase in the endurance limits for the specimens with stress concentration factors K _t?=?1.91 and 3.91, respectively. The notch sensitivity of 316L steel reduced after carburisation. Irrespective of the applied stress amplitude, the fatigue crack nucleation sites were always at the notch root surface for the untreated specimens. For the carburised specimens, fatigue cracks nucleation changed from surface at high-level stress to subsurface at low-level stress.     

Numerical analysis of the stress intensity factors for repaired cracks from a notch with bonded composite semicircular patch

In this paper, we investigated the crack growth behaviour of cracked thin aluminium plate repaired with bonded composite patch. The finite element method is used to study the performance of the bonded composite reinforcement or repair for reducing the stress concentration at a semicircular lateral notch and repairing cracks emanating from this kind of notch. The effects of the adhesive properties and the patch size on the stress intensity factor variation at the crack tip in mode I were highlighted. The obtained results show that the stress concentration factor at the semicircular notch root and the stress intensity factor of a crack emanating from notch are reduced with the increase of the diameter and the number of the semicircular patch. The maximal reduction of stress intensity factor is about 42% and 54%, respectively, for single and double patch. However, the gain in the patch thickness increases with the increase of the crack length and it decreases when the patch thickness increases. The adhesive properties must be optimised in order to increase the performance of the patch repair or reinforcement.     

Observations of the micro-mechanisms of fatigue-crack initiation in polycarbonate

The mechanisms of crack initiation in tensile fatigue of single-edge notched specimens of polycarbonate of varying thickness have been elucidated. At low stresses and long times microcracking and localized yielding occurred to form regular diamond-shaped cells on a scale of 2–4 m. On increasing the stress level with thin specimens (<1 mm), the microshear bands coalesced to form macroscopic damage zones of yielded material around the notch, followed by crack tearing from the notch surface. With increasing specimen thickness, restriction of shear banding ensued and a stable, semi-elliptical cavitation, or pop-in, formed about 10–100 m ahead of the notch, dependent on specimen geometry. As a result, the ligament formed between the notch and pop-in consists of yielded material. Brittle behaviour resulted with further increases in specimen thickness on loading, i.e. when the ligament could not be stabilized.     

Fundamental solutions for an anisotropic medium with a notch or an inclusion

Abstract

A fundamental solution for an anisotropic medium with a notch or a rigid inclusion of arbitrary shape is derived based on the complex potential formulation of anisotropic elasticity. The solutions for a crack, for a circular hole or inclusion, and for a half plane are obtained as special cases. The solution can be applied to the analysis of crack, notch and inclusion problems of anisotropic materials.     

A microscopic study of crack initiation mechanisms in 7075 aluminum alloy sheets

A study of the opening mode of crack initiation in 7075-T6 aluminum alloy sheets has been conducted with the aid of a scanning electron microscope. Observations were made from several orientations including the top view of the specimen which showed the notch profile and the edge view of the specimen which showed the entire notch front along the specimen thickness. It was found that the edge view exhibited the first signs of permanent deformation at about 55 per cent of the breaking strength. These changes took the form of deformation bands which were aligned in the direction of the tensile axis and apparently defined limiting regions of homogeneous slip. It is felt that the appearance of microcracks at loads approaching the breaking strength was of fundamental importance in the formation of the final fracture surface. Many of these microcracks were initiated at intermetallic particles and other metallurgically weak regions on the notch surface. It was also possible to correlate the strain in the notch with the stress intensity factor for the various loads. Very large plastic strains were observed on the notch tip as compared to published values of elongation at fracture for unnotched specimens.     

Fatigue of Kaowool reinforced aluminum: Effect of shot particle wall thickness

The fatigue performance of Kaowool fiber reinforced 339 aluminum composites at 300°C is limited by spherical thin walled hollow Kaowool shot particles. These act as crack initiation sites particularly when located at the surface. This problem does not occur for thick walled particles or particles filled with the aluminum matrix. The effect of wall thickness (t) is evaluated from finite element analysis of both 2D and 3D models, with and without plasticity. Both models predict that hollow thin walled particles act as defects, while thick walled particles act as reinforcements, this transition being defined by a critical wall thickness (t _c). The 3D model is preferred in that it predicts more accurate and smaller values of t _c. Specifically, the 3D elastic/plastic model predicts that the largest stress concentration occurs for a fractional surface particle and that in this condition t _c = 0.18a, where a is the particle radius. This value agrees with our experimental observation that particles with t > 0.2a do not initiate failures.     

Generalized plane problem of a cracked piezoelectric layer bonded to dissimilar layers

Summary In this paper, we proposed a model to study the electro-elastic crack problem for a cracked piezoelectic layer bonded to two elastic layers of finite thickness. The crack is assumed to be through thez-direction and the crack faces perpendicular to they-direction. Fourier transforms technique is used to reduce the problem to the solution of singular integral equations. The model is general enough to account for arbitrary electrical polarized direction and material anisotropy, for any mechanical or electrical mode of loading. Numerical results are plotted to illustrate the influence of the crack face electrical boundary condition on crack tip fields for different layer thickness.     

Surface topography evolution and fatigue fracture of polysilicon

This paper presents the results of an experimental stydy of the micromechanisms of fatigue crack nucleation and fatigue fracture in polysilicon MEMS Structures. The initial stages of fatigue are shown to be associated with stress-assisted surface topography evolution and the thickening of SiO₂ layers that form on the unpassivated polysilicon surfaces and crack/notch faces. The differences in surface topography and oxide thickness are elucidated as functions of fatigue cycling before discussing the micromechanisms of crack growth and final fracture.     

Fatigue growth of short cracks in Ti-17: Experiments and simulations

The fatigue behaviour of through thickness short cracks was investigated in Ti-17. Experiments were performed on a symmetric four-point bend set-up. An initial through thickness crack was produced by cyclic compressive load on a sharp notch. The notch and part of the crack were removed leaving an approximately 50 μm short crack. The short crack was subjected to fatigue loading in tension. The experiments were conducted in load control with constant force amplitude and mean values. Fatigue growth of the short cracks was monitored with direct current potential drop measurements. Fatigue growth continued at constant R-ratio into the long crack regime. It was found that linear elastic fracture mechanics (LEFM) was applicable if closure-free long crack growth data from constant K_Imax test were used. Then, the standard Paris’ relation provided an upper bound for the growth rates of both short and long crack.The short crack experiments were numerically reproduced in two ways by finite element computations. The first analysis type comprised all three phases of the experimental procedure: precracking, notch removal and fatigue growth. The second analysis type only reproduced the growth of short cracks during fatigue loading in tension. In both cases the material model was elastic-plastic with combined isotropic and kinematic hardening. The agreement between crack tip opening displacement range, cyclic J-integral and cyclic plastic zone at the crack tip with ΔK_I verified that LEFM could be extended to the present short cracks in Ti-17. Also, the crack size limits described in the literature for LEFM with regards to plastic zone size hold for the present short cracks and cyclic softening material.     

A note on Orowan mechanism below the root of an yielding crack like notch in a strain-hardening metal

Based on Orowan's historic model, a local fracture initiation criterion is proposed for high strength strain-hardening metals. A crack like notch geometry is studied in the following Von Mises yielding materials: (a) an ideally plastic-elastic solid, and (b) a power law strain-hardening metal. Orowan mechanism is seen to be dominant below the root region of an yielding crack like notch, just before the onset of fracture. Close to the elastic-plastic interface, Orowan's Kink-band forms inside the plastic region, when a mismatch Kink-stress (in radial component only) reaches a critical value in this particular region. It is extremely important to note that, this narrow Kink-band zone, where the micro-cracks are likely to nucleate, lies at a distance approx. $\text{3}\text{4}\text{s}$, where s is the size of the plastic zone on the crack extension plane under a plane strain deformation. A reverse slip mechanism operates in this region in addition to the presence of a pure hydrostatic tension, just before the release of this critical Kink-stress. Due to this stress history, a large inhomogeneous strain-localization occurs in a narrow band, which could then interact with the free notch surface before the onset of final instability. Thus, at the onset of crack extension, (satisfying Griffith-Irwin criterion of fracture), the stress intensification at the notch tip root is directly proportional to the strength of this critical strain-localization and inversely proportional to the plastic zone size on the crack extension plane. Hence, it is concluded that: Orowan's mechanism and McClintock's criteria for critical strain-localizations should play the most important roles for predicting the local fracture behaviour of metals.     

A NEW METHOD FOR PREDICTING FATIGUE LIFE IN NOTCHED GEOMETRIES

The objective of this paper is to develop a notch crack closure model, called NCCM, based on plasticity-induced effects and short fatigue crack growth in the vicinity of the notch, and to predict the fatigue failure life of notched geometries. By using this model the regime for non-propagating cracks (n.p.c.) and the relationship between the fatigue strength reduction factor, Kf , and the elastic stress concentration factor, Kt , under mean stress conditions, can be determined quantitatively. A crack closure model is assumed to apply in the notch regime based on an approach developed to explain the crack growth retardation behavior observed in smooth specimen geometries after an overload. Notch plasticity effects are also applied in the NCCM model. Fatigue failure life is calculated from both short fatigue crack growth in the notch region where elastic–plastic fracture mechanics (EPFM) is applied and from long fatigue crack growth remote from the notch where linear elastic fracture mechanics (LEFM) occurs. This prediction is obtained using a quantity called the effective plasticity-corrected pseudo-stress. The NCCM can be used to account quantitatively for various observed notch phenomena, including both the relationship between Kf and Kt and n.p.c. The effects of the tensile mean stress on the Kf versus Kt relationship is investigated and leads to the little recognized but technologically important observation that mean stress conditions exist where Kf can be greater than Kt . The role of notch radius and tensile mean stress on n.p.c. behavior is also explored. The model is verified using experimental data for notch geometries of aluminum alloy 2024-T3, alloy steel SAE 4130 and mild steel specimens tested at zero and tensile mean stress.     

The growth of short fatigue cracks ahead of a notch in high strength steel

This paper is concerned with the short crack growth behaviour in notched specimens of high strength steels mainly used for automotive parts. Attention is focused on the appropriate estimation of the stress intensity range ΔK, when the short cracks grow in the stress field of a notch and attempts are made to investigate whether this is appropriate or whether further allowance may have to be made for short crack effects at low ΔK.The stress distribution for the notch in bending was taken into account for the estimation of ΔK. This enabled us to produce a more precise evaluation of short crack growth in the stress field of the notch. Our findings are that the short cracks, which propagate in the notch field, grow faster at low ΔK when their lengths are extremely short compared with the notch root radius. The short crack effect at low ΔK in the notch stress field is analysed by expressing the crack growth data in terms of the parameter, ΔK_s, in which stress gradient ahead of the notch is taken into account.     

Estimation of fatigue crack propagation life of steel plates and of structural member model of ship hull

The authors carried out experimental and analytical investigation for the purpose of finding out a method of estimating the fatigue crack propagation life of large flat steel plate and of ship hull structure model quantitatively.We theoretically derived a formula indicating that fatigue crack propagation rate is in proportion to the $\text{m-}\text{th}$ power of the plastic displacement of the tip of a crack based on a B.C.S. dislocation model. The crack propagation rate is proportional to $\text{2m-}\text{th}$ power of stress intensity factor in the case stress is small.We proved experimentally that this relation holds generally, from fatigue crack propagation tests for flat plates with a center notch (mild steel, high tensile strength steel), large flat plate with an edge notch and ship hull corner model (mild steel), and from the $\text{K-}\text{value}$ calculation by the finite element method for these specimens. The fatigue crack propagation life is obtained by integrating the reciprocal number of crack propagation rate from the initial crack length to the final crack length. The life calculated agreed well with the one observed. But for the two stress level test, the life calculated was smaller than the experimental value due to slackened progress of crack. We also stated the general characteristics of the rate curve.     

The problem of sharp notch in microstructured solids governed by dipolar gradient elasticity

In this paper, we deal with the asymptotic problem of a body of infinite extent with a notch (re-entrant corner) under remotely applied plane-strain or anti-plane shear loadings. The problem is formulated within the framework of the Toupin-Mindlin theory of dipolar gradient elasticity. This generalized continuum theory is appropriate to model the response of materials with microstructure. A linear version of the theory results by considering a linear isotropic expression for the strain-energy density that depends on strain- gradient terms, in addition to the standard strain terms appearing in classical elasticity. Through this formulation, a microstructural material constant c is introduced, in addition to the standard Lamé constants (λ, μ). The faces of the notch are considered to be traction-free and a boundary-layer approach is followed. The boundary value problem is attacked with the asymptotic Knein-Williams technique. Our analysis leads to an eigenvalue problem, which, along with the restriction of a bounded strain energy, provides the asymptotic fields. The cases of a crack and a half-space are analyzed in detail as limit cases of the general notch (infinite wedge) problem. The results show significant departure from the predictions of the standard fracture mechanics.     

A 'crack-like' notch analogue for a safe-life fretting fatigue design methodology

Various analogies have recently been proposed for comparing the stress fields induced in fretting fatigue contact situations, with those of a crack and a sharp or a rounded notch, resulting in a degree of uncertainty over which model is most appropriate in a given situation. However, a simple recent approach of Atzori–Lazzarin for infinite‐life fatigue design in the presence of a geometrical notch suggests a corresponding unified model also for fretting fatigue (called Crack‐Like Notch Analogue model) considering only two possible behaviours: either ‘crack‐like’ or ‘large blunt notch.’ In a general fretting fatigue situation, the former condition is treated with a single contact problem corresponding to a Crack Analogue model; the latter, with a simple peak stress condition (as in previous Notch Analogue models), simply stating that below the fatigue limit, infinite life is predicted for any size of contact. In the typical situation of constant normal load and in phase oscillating tangential and bulk loads, both limiting conditions can be readily stated. Not only is the model asymptotically correct if friction is infinitely high or the contact area is very small, but also remarkably accurate in realistic conditions, as shown by excellent agreement with Hertzian experimental results on Al and Ti alloys. The model is useful for preliminary design or planning of experiments reducing spurious dependences on an otherwise too large number of parameters. In fact, for not too large contact areas (‘crack‐like’ contact) no dependence at all on geometry is predicted, but only on three load factors (bulk stress, tangential load and average pressure) and size of the contact. Only in the ‘large blunt notch’ region occurring typically only at very large sizes of contact, does the size‐effect disappear, but the dependence is on all other factors including geometry.