Cooperative cavitation in rubber-toughened polycarbonate

Particle cavitation in the stress-whitened zone ahead of a semicircular notch in polycarbonate blended with a core-shell rubber was characterized by transmission electron microscopy. Cavitation of rubber particles at five locations in the stress-whitened zone was correlated with the local stress and strain history. It was found that cavitation initiated some distance ahead of the notch when a mean stress condition was met. Initially, only a fraction of the particles cavitated and these were randomly distributed. Single cavitated particles grew into cavitated domains by cooperative cavitation of nearby particles until cavitation was arrested when shear yielding of the matrix provided an alternative mechanism for relief of strain energy. Far from the notch, where the stress state approached uniaxial tension, cavitated domains grew into linear arrays of cavitated particles. A mechanism of cooperative crazing in microlayer composites of polycarbonate and styrene/acrylonitrile copolymer was adapted to cooperative cavitation of core-shell rubber particles. It was proposed that cooperative cavitation of nearby particles occurred by impingement of a small plastic zone that formed at the equator of a cavitated particle.     

Fracture of notched polycarbonate under hydrostatic pressure

The brittle fracture behaviour and plastic deformation of round-notched polycarbonate bars subjected to three-point bending under hydrostatic pressure have been studied. Below a certain critical pressure, the brittle fracture initiated from an internal craze nucleated at the tip of the local plastic zone ahead of the notch rooT. The position of the nucleation of the craze receded from the tip of the notch with increasing applied pressure. When the pressure was increased over a critical value, general yielding occurred by passage of the plastic zone across the notched cross-section, that is, the brittle to ductile transition took place. A qualitative analysis of the stress distribution within the plastic zone explains that the brittle to ductile transition under hydrostatic pressure occurs when the general yield takes place before a critical stress for brittle crack propagation is reached.     

CORRELATION BETWEEN HYDROGEN INDUCED CRACKING INITIATION SITES AND CRITICAL STRESS INTENSITY FACTORS

Hydrogen induced cracking (HIC) initiation sites and their correlation with the critical stress intensity factors of hydrogen charged specimens were studied under combined I/II mode loading. Two series of tests, is. constant load (CL) tests and slow strain rate (SSR) tests, were carried out. Experimental results showed that in CL tests, irrespective of the ratio KIJKl, the HIC initiation sites always correspond to the point of maximum hydrostatic stress; which is located some distance ahead of the notch tip. However, for SSRT tests, when K₁₁/K₁> 1, HIC started at the notch tip which corresponds to the point of maximum equivalent plastic strain. When K₁₁/K₁<1 in SSR tests, HIC occurred initially some distance ahead of the notch tip. The relationship between the critical stress intensity factor for HIC and K₁₁/K₁ was shown to be different for the two types of test. Multiple effects of stress and strain on hydrogen redistribution and hence on HIC initiation sites, as well as critical stress intensity factors, are discussed.     

Analytical study of the elastic–plastic stress fields ahead of parabolic notches under antiplane shear loading

An analytical study is carried out on the elastic–plastic stress and strain distributions and on the shape of the plastic zone ahead of parabolic notches under antiplane shear loading and small scale yielding. The material is thought of as obeying an elastic-perfectly-plastic or a strain hardening law. When the notch root radius becomes zero, the analytical frame matches the solutions for the crack case due to Hult–McClintock (elastic-perfectly-plastic material) and Rice (strain hardening material). The analytical frame provides an explicit link between the plastic stress and the elastic stress at the notch tip. Neuber’solution for blunt notches under antiplane shear is also obtained and the conditions under which such a solution is valid are discussed in detail by using elastic and plastic notch stress intensity factors. Finally, revisiting Glinka and Molski’s equivalent strain energy density (ESED), these factors are used also to give, under antiplane shear loading, the increment of the strain energy at the notch tip with respect to the linear elastic case.     

Size effect in fracture of unidirectional composite plates

Fracture of notched, unidirectionally reinforced composite plates with well-bonded ductile matrices is typically preceded by the formation of long, discrete plastic shear zones aligned in the fiber direction. Onset of fracture is associated with a critical tension stress in a certain small process zone ahead of the notch tip; the critical stress is often equal to the tensile strength of the unnotched composite plate. Length of the shear zones can be estimated by plastic limit-analysis, and the local tension stress ahead of the notch found by superposition of the stress caused by remotely applied loads with the stress induced by the shear tractions in the plastic zone, which is shown to be dominated by a logarithmic singularity. In as-fabricated boron-aluminum composites, this fracture mechanism was analyzed and confirmed by numerous experiments (G.J. Dvorak, J. Zarzour and Y. Benveniste, Engineering Fracture Mechanics 42, 501–517, 1992). Since the notch tip field is not described by a stress intensity factor, experimental notched strength data cannot be interpreted in terms of a single material property, such as toughness. An alternative scaling procedure is outlined for prediction of notched strength of wide plates on the basis of data obtained from small size specimens. This revised version was published online in July 2006 with corrections to the Cover Date.     

Is stress concentration relevant for nanocrystalline metals?

Classical fracture mechanics as well as modern strain gradient plasticity theories assert the existence of stress concentration (or strain gradient) ahead of a notch tip, albeit somewhat relaxed in ductile materials. In this study, we present experimental evidence of extreme stress homogenization in nanocrystalline metals that result in immeasurable amount of stress concentration at a notch tip. We performed in situ uniaxial tension tests of 80 nm thick (50 nm average grain size) freestanding, single edge notched aluminum specimens inside a transmission electron microscope. The theoretical stress concentration for the given notch geometry was as high as 8, yet electron diffraction patterns unambiguously showed absence of any measurable stress concentration at the notch tip. To identify possible mechanisms behind such an anomaly, we performed molecular dynamics simulations on scaled down samples. Extensive grain rotation driven by grain boundary diffusion, exemplified by an Ashby-Verrall type of grain switching process, was observed at the notch tip to relieve stress concentration. We conclude that in the absence of dislocations, grain realignment or rotation may have played a critical role in accommodating externally applied strain and neutralizes any stress concentration during the process.     

Corrosion-Facilitating Local Plastic Deformation for α-Ti in Methanol

The effect of corrosion process on facilitating local plastic deformation for α-Ti in methanol has been investigated with the micro-multiplicative moire interferometer technique. The size of plastic zone and the plastic strain ahead of loaded notch have been measured. The results show that the anodic dissolution, or corrosion process itself can enhance the plastic zone and the plastic strain ahead of a loaded notch during stress corrosion of α-Ti in methanol solution     

Effects of notch geometry on the local cleavage fracture stress σf

An elastic–plastic finite element method (FEM) is used to analyse the stress and strain distributions ahead of notches with various depths and flank angles in four-point bending (4PB) specimens of a C–Mn steel. By accurately measuring the distances of the cleavage initiation sites from the notch roots, the local cleavage fracture stress σ _f is measured. By increasing the notch depth and notch flank angle from 2.25 to 8.25 mm and 10 to 90°, respectively, the distributions of high stress and strain at the moment of fracture show considerable variations. However, the value of σ _f stays relatively constant. The critical fracture event is thus shown to be identical, i.e. the propagation of a ferrite grain-sized crack into the neighbouring matrix. It is concluded that σ _f is mainly determined by the length of the critical microcrack, while the notch geometry and its associated stress volume have little effect on the value of σ _f . The cleavage site ahead of a notch is determined by the stress distributions and the positions of the weakest grains.     

Failure of a Porous Solid from a Deep Notch

A finite strain finite element method is used to examine the stress state near the tip of a deep notch in an elastic-plastic porous solid. The notch is loaded in mode I plane strain tension and small scale yielding is assumed. Two rate independent strain hardening material models are used: a version of the Gurson model (1977) and the more recent FKM model developed by Fleck, Kuhn and McMeeking (1992). Under increasing K _I, void growth is initially stable and independent of mesh dimension. Localization of plastic flow sets in at a finite value K _i, and the deformation field is mesh-size dependent thereafter. The initiation of crack growth at the notch root is assumed to occur when a critical level of porosity is attained. The results show that the shape of the plastic zone for both the Gurson and the FKM material is highly dependent on the initial porosity. In the case of low initial porosity, the plastic zone shape is similar to that of a fully dense material; at higher initial porosities the plastic zone is concentrated ahead of the notch tip. The effect of the initial void volume fraction on the porosity field and the critical stress intensity factor is studied, and the mesh-size dependence of the results is discussed. The analysis is useful for prediction of the notched strength of porous metals. This revised version was published online in August 2006 with corrections to the Cover Date.     

Analysis of elastoplastic sharp notches

In this paper the elastoplastic solutions with higher-order terms for apex V-notches in power-law hardening materials have been discussed. Two-term expansions of the plane strain and the plane stress solutions have been obtained. It has been shown that the leading-order singularity approaches the value for a crack when the notch angle is not too large. In plane strain cases the elasticity does not enter the second-order solutions when the notch opening angle is too small. For a large notch angle, the two-term expansions of the plane strain near-tip fields are described by a single amplitude parameter. The plane stress solutions generally contain the elasticity terms. The boundary layer formulations based on the small-strain plasticity theory confirm that a dominance zone exists ahead of the notch tip. Finite element results give good agreement to the asymptotic solutions under both plane strain and plane stress conditions. The second-order terms cannot improve the predictions significantly. The near-tip fields are dominated by a single parameter. Finite element calculations under the finite strain J ₂-flow plasticity theory revealed that the finite strains can only affect local characterization of the asymptotic solution. The asymptotic solution has a large dominance zone around the notch tip. For an apex notch bounded to a rigid substrate the leading-order singularity falls with the notch angle significantly more slowly than in the homogeneous material. It vanishes at the notch angle about 135° for all power-hardening exponents. The elasticity effects enter the second-order solutions when the notch angle becomes large enough. The tip fields are characterized by the hydrostatic stress and the shear stress ahead of the notch.     

Effects of loading rate on the local cleavage fracture stress σf in notched specimens

Four point bending (4PB) notched specimens with different notch sizes are tested at various loading rates at a temperature of −110 °C for a C-Mn steel. An elastic-plastic finite element method (FEM) is used to determine the stress and strain distributions ahead of notches. By accurately measuring the distances of the cleavage initiation sites from the notch roots, the local cleavage fracture stress σ_f is measured. The results show that the local cleavage fracture stress σ_f does not essentially change with loading rate V and notch size. The reason for this is that the cleavage micromechanism does not change in the different specimens at various loading rates. The cleavage micromechanism involves competition of two critical events of crack propagation and crack nucleation in the high stress and strain volume ahead of notch root. The large scatter of σ_f and notch toughness are mainly caused by the different critical events in different specimens.     

Generalized stress intensity factors due to steady and transient thermal loads with applications to welded joints

This paper deals with the elastic and plastic stress fields induced by thermal loads in the vicinity of sharp V‐notch tips in plates. Under the hypothesis of steady‐state heat transfer and plane‐strain conditions, the thermal and mechanical problem requires the numerical solution of an ordinary differential equation (ODE) system, obtained by extending the ‘stress function approach’. The intensity of the stress distributions ahead of V‐notch tips can be expressed in terms of thermal notch stress intensity factors (thermal NSIFs), as for external loads. The problem becomes much more demanding in the presence of transient thermal loads. The residual asymptotic stress distribution arising from the solidification of a fusion zone during an arc welding process is obtained by considering different boundary conditions. An aluminium butt‐welded joint is analysed after having modelled the weld toe region as a sharp V‐notch. A finite element (FE) simulation of the welding process is carried out by means of SYSWELD code (version 2004.1) modelling the arc welding torch by means of Goldak's source. Near the weld toe, the intensity of the residual stress field is given in terms of elastic or elastic—plastic generalized NSIFs.     

Microstructure-dependent fatigue damage process zone and notch sensitivity index

The development of simulation methods for calculating notch root parameters for purposes of estimating the fatigue life of notched components is a critical aspect of designing against fatigue failures. At present, however, treatment of the notch root stress and plastic strain field gradients, coupled with intrinsic length scales of grains or other material attributes, has yet to be developed. Ultimately, this approach will be necessary to form a predictive basis for notch size effects in forming and propagating microstructurally small cracks in real structural materials and components. In this study, computational micromechanics is used to clarify and distinguish process zone for crack formation and microstructurally small crack growth, relative to scale of notch root radius and spatial extent of stress concentration at the notch. A new nonlocal criterion for the fatigue damage process zone based on the distribution of a shear-based fatigue indicator parameter is proposed and used along with a statistical method to obtain a new microstructure-sensitive fatigue notch factor and associated notch sensitivity index, thereby extending notch sensitivity to explicitly incorporate microstructure sensitivity and attendant size effects via probabilistic arguments. The notch sensitivity values obtained for a range of notch root radii using the new statistical approach presented in this study predict the general trends obtained from experimental results available in literature.     

The cohesive zone model in a problem of delayed hydride cracking of zirconium alloys

The crack tip model with the cohesive zone ahead of a finite crack tip has been presented. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration, according to Westergaard's theory, with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. Local criterion of brittle fracture and modelling of the fracture process zone by cohesive zone were used to describe fracture initiation at the hydride platelet in the process zone ahead of the crack tip. It was shown that the theoretical K _IH-estimation applied to the case of mixed plane condition within the process zone is qualitatively consistent with experimental data for unirradiated Zr-2.5Nb alloy. In the framework of the proposed model, the theoretical value of K ^H _IC for a single hydride platelet at the crack tip has been also estimated.     

On the slope of the fatigue resistance curve for laser stake‐welded T‐joints

The paper investigates the influence of highly localised stress distribution around the notch tips of the laser stake‐welded T‐joints to the slope of the fatigue resistance curve. The study considers experimental data of eight series involving joints under tension or bending loads. Various boundary conditions and plate thicknesses are considered. The stress distribution in the singularity‐dominated zone ahead of the notch tips is investigated by means of the finite element analysis. The aim is to relatively distinguish the stress distribution from one case to another. The growth rate of the elastic singular stress with respect to the distance from the tip is described by the dimensionless gradient. This gradient is equal to the slope of the linear stress‐distance function when presented in double‐logarithmic scale. The slope of the fatigue resistance curve varies approximately from 4 to 8. It is observed that the change of the slope can be closely associated with the gradient of the maximum principal stress evaluated in the plane that is orthogonal to the crack path. The orthogonal plane corresponds to the maximum principal stress direction. In contrast, there is a large scatter in the relation between the slope and the gradient evaluated in the commonly assumed crack plane. The study shows that the dimensionless gradient exhibits sensitivity towards plate thicknesses, local weld geometry and the loading condition.     

Ratcheting progress at notch root of 1045 steel samples over asymmetric loading cycles: Experiments and analyses

The present study examines ratcheting response of steel samples with various notch diameters through conducting several cyclic tests. Ratcheting strain values were measured through strain gauges mounted at different distances from the notch root. Local ratcheting at the notch region was highly influenced by notch diameter, notch shape, distance from the notch root, and magnitude of the nominal mean/amplitude of loading cycles. Nominal force‐controlled cycles were kept below the yield point and the Neuber's rule accommodated for the maximum/minimum local stress components along those local strains measured through the strain gauges at the notch region. Plastic strains at the vicinity of notch root over loading cycles were further accumulated by means of the Chaboche hardening model. The local ratcheting strain while progressed at the notch root plastic zone over loading cycles resulted in mean stress relaxation controlled by the model.     

The cohesive zone model in a problem of delayed hydride cracking of zirconium alloys

The crack tip model with the cohesive zone ahead of a finite crack tip has been presented. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration, according to Westergaard's theory, with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. Local criterion of brittle fracture and modelling of the fracture process zone by cohesive zone were used to describe fracture initiation at the hydride platelet in the process zone ahead of the crack tip. It was shown that the theoretical K _IH-estimation applied to the case of mixed plane condition within the process zone is qualitatively consistent with experimental data for unirradiated Zr-2.5Nb alloy. In the framework of the proposed model, the theoretical value of K ^H _IC for a single hydride platelet at the crack tip has been also estimated.     

EFFECT OF NOTCH STRESS FIELD AND CRACK CLOSURE ON SHORT FATIGUE CRACK GROWTH

Abstract— The growth rate of a short fatigue crack that is partly or wholly embedded within the notch plastic zone, is affected by the extent and intensity of the elastic-plastic notch stress field and closure effect. The notch stress—strain field and plastic zone were analysed by the Finite Element Method (FEM). The growth rate and the closure curve for a short fatigue crack emanating from the notch root were measured. Based on the experimental and numerical analyses, a modified Linear Elastic Fracture Mechanics (LEFM) parameter is proposed for a short through-thickness crack emanating from a notch root under elastic—plastic loading conditions.     

A stress distribution remodelling technique

The stress distribution ahead of a notch is of great practical interest when undertaking fatigue and fracture analyses. In particular it is generally the first principal stress close to the notch which is desired. For a sharp notch this can be characterized by the stress field parameter K ^N which is referred to as the notch stress intensity factor (or N-SIF). The finite element method is a very powerful tool which is commonly used to determine K ^N . However, unless specialized methods are used the finite element mesh must be extremely refined in the region of the notch in order to calculate an accurate value. In practical situations, the degree of mesh refinement necessary is often not possible, due to either time or computer limitations. The following describes a simple technique which can be used to accurately determine the stress distribution close to a sharp notch, by remodelling or reshaping a stress distribution that has been obtained from a finite element analysis using a coarse or inadequate mesh. A theoretical equation for defining the principal stress distribution ahead of a sharp notch, which has been developed by Atzori et al. (2005) is used to do this. It is shown that the theoretical distribution can be explicitly determined from the finite element distribution by using global equilibrium conditions. It is shown that this technique is independent of the finite element mesh size. The method is used to calculate K ^N for seven different combinations of geometry and loading condition, using various FE mesh refinement. It is shown that the results are accurate to within 15%.     

Fatigue life prediction of small notched Ti-6Al-4V specimens using critical distance

This study investigated the method of estimating the fatigue strength of small notched Ti-6Al-4V specimen using the theory of critical distance that employs the stress distribution in the vicinity of the notch root. Circumferential-notched round-bar fatigue tests were conducted to quantify the effects of notch radius and notch depth on fatigue strength. The fatigue tests show that the larger notch radius increases the fatigue strength and the greater notch depth decreases the fatigue strength. The theory of critical distance assumes that fatigue damage can be correctly estimated only if the entire stress field damaging the fatigue fracture process zone is taken into account. Critical distance stress is defined as the average stress within the critical distance from notch root. The region from the notch root to the critical distance corresponds to the fatigue fracture process zone for crack initiation. It has been found that a good correlation exists between the critical distance stress and crack initiation life of small notched specimens if the critical distance is calibrated by the two notched fatigue failure curves of different notch root radii. The calibrated critical distances did not vary clearly over a wide range of fatigue failure cycles from medium-cycle low-cycle fatigue regime to high-cycle fatigue regime and have an almost constant value. This critical distance corresponds to the size of crystallographic facet at the fatigue crack initiation site for the wide range of fatigue cycles.