External Crack Research Articles

Probabilistic Critical Fatigue Safety State of the RD2 Type Axle of China Railway Freight Car

Critical fatigue safety state is investigated on RD2 type axle of China railway freight cars. Attention is paid on the grooves near axle boxes, where more fatigue cracks were early appeared even result in at least six derailed accidents. Load history was obtained by vehicle dynamics simulation combining with on-line inspection. Braking loads and effects of maintenance and off-round of wheels are also incorporated. Semi-elliptical and external circumferential cracks are employed for crack growth simulation. Crack shape change and shear stressing of the semi-elliptical crack are taken into account. New crack growth rate modeling in which covers from cracking threshold to toughness related fracture state is applied for residual life evaluation. Critical fatigue safety state is defined as the crack size from which the axle can be safely operated to next overhaul inspection. Critical crack size is estimated step-by-step with the crack shape change. Results show that the external circumferential crack is more dangerous than the semi-elliptical crack. Application more than two years in production verifies that the present assessment is available and reliable.

Secondary cooling of continuous-cast billet at OOO Uralmash-Engineering

modifying the thickness and mechanical properties of the ingot crust. However, this often leads to the formation and development of surface cracks, especially edge, reticular, and transverse cracks. Thus, by selecting different cooling rates, the temperature gradient and the temperature stress and strain at the outer surface and solidification front may be adjusted, and the brittleness range may be avoided. A compromise value must be sought here, since increasing the temperature gradients is favorable in terms of compressive stress and strain at the center of the billet but also tends to increase the tensile stress and strain at the outer surface. At most Russian metallurgical enterprises, quality requirements are formulated in terms of axial porosity, axial chemical inhomogeneity, internal cracks (perpendicular to the broad or narrow faces, axial cracks, pitlike cracks), and external cracks (longitudinal, transverse, edge, and reticular). The appearance of such cracks is due to complex factors, most notably the derivatives of the thermal stress and stress-strain state with respect to the mechanical loads. Manufacturers of continuous-casting machines employ different approaches to cooling.

CASTA DIVA®: Experiments and Modeling of Oxide-Induced Deformation in Nuclear Components

Abstract In-pile deformation of nuclear structural components remains a major preoccupation for fuel vendors and utilities, especially when introducing new alloys or extending burn-ups. The usual invoked causes of such deformations are free growth, hydriding (hydrides induce a volume expansion which translates into deformation), irradiation creep if the component is subjected to external loads (e.g., axial load for the fuel assembly), and flux gradients (for fuel channel bow). In this paper we show through out-of-pile experiments (autoclave corrosion and low temperature air oxidation) and in-pile data analysis that the oxide layer significantly contributes to the deformation. A model (CASTA DIVA®) taking into account all the above mentioned phenomena has been derived and correctly predicts the deformation behavior, the stresses in the oxide layer, as well as the external cracking of the oxide. The relative impacts of hydriding and stresses in the metal are computed. A comparison between Zircaloy-4 and M5® is made, showing the better behavior of M5.

Search for scutellonema bradys resistance in yams (dioscorea spp.)

A study to examine variability in susceptibility of yams to Scutellonema bradys and to identify possible sources of resistance in Ghanaian yam germplasm (Dioscorea spp.) for use in yam improvement programmes, particularly, in West Africa was undertaken. Pot and field screening methodologies were used. In general, S. bradys and dry rot of tuber symptoms as well as tuber cracking increased during the storage period. The study showed a positive correlation between visual nematode damage and population densities in yam tubers. There was also a linear relationship between dry rot disease and tuber cracking at harvest and during storage. This confirms that S. bradys causes dry rot of tubers resulting in external cracking of yam tubers. Positive linear relationship was also observed between yam tuber weight loss and dry rot disease indicating that dry rot disease may have contributed to the tuber weight loss. Therefore, tuber dry rot symptoms caused by S. bradys of yams could be used to discard susceptible yams at harvest and after a period of storage. However, there was no linear relationship between nematode population densities in yam tubers and roots, therefore, a root protocol cannot be used for assessing resistance in yams as it could lead to misclassification. The yam germplasm screened, reaffirmed resistance to S. bradys in Dioscorea dumetorum var. Nkanfo and D. cayenensis var. Afun.

Influence of flow stress choice on the plastic collapse estimation of axially cracked steam generator tubes

The influence of the choice of flow stress on the plastic collapse estimation of axially cracked steam generator (SG) tubes is considered. The plastic limit and collapse loads of thick-walled tubes with external axial semi-elliptical surface cracks are investigated by three-dimensional non-linear finite element (FE) analyses. The limit pressure solution as a function of the crack depth, length and tube geometry has been developed on the basis of extensive FE limit load analyses employing the elastic–perfectly plastic material behaviour and small strain theory. Unlike the existing solutions, the newly developed analytical approximation of the plastic limit pressure for thick-walled tubes is applicable to a wide range of crack dimensions. Further, the plastic collapse analysis with a real strain-hardening material model and a large deformation theory is performed and an analytical approximation for the estimation of the flow stress is proposed. Numerical results show that the flow stress, defined by some failure assessment diagram (FAD) methods, depends not only on the tube material, but also on the crack geometry. It is shown that the plastic collapse pressure results, in the case of deeper cracks obtained by using the flow stress as the average of the yield stress and the ultimate tensile strength, can become unsafe.

Normal and tangential compliances of interface of rough surfaces with contacts of elliptic shape

The incremental compliances, normal and tangential, of an interface between rough surfaces are considered. Contacts are assumed to be elliptic – the shape of Hertzian contacts between any two locally smooth asperities. The ellipses may have diverse eccentricities and random or non-random orientation distribution; in the latter case, the tangential compliance is anisotropic. It is found that the Hertzian contacts and “welded” zones of the same geometry produce the same incremental compliances. Microstructural characteristics ξ of the interface that controls its incremental compliances is identified. For the circular contacts, ξ is the sum ∑ A k where A k is kth contact area; in the more general case of elliptic contacts, each A k enters in product with its shape factor dependent on the ellipse aspect ratio. The mentioned in-plane tangential anisotropy is relatively mild, even for parallel strongly elongated elliptic contacts. This is due to weakness of the anisotropy for a single elliptic contact (or external elliptic crack). Comparison of the latter to the internal crack of the same elliptic geometry shows that whereas the anisotropy is mild for both crack types, it is weaker for the external crack, in which case it is also less sensitive to Poisson’s ratio.

Stress Intensity Factors Analyses of a Three-Dimensional Interface Crack Between Anisotropic Dissimilar Materials Under Thermal Stress

A new numerical method was presented for stress intensity factors (SIFs) analyses of a three-dimensional interface crack between dissimilar anisotropic materials subjected to thermal stress. The M-integral method was applied to the thermoelastic interfacial crack in three-dimensional anisotropic bimaterials. The moving least square method was used to calculate the value of the M-integral. The M-integral in conjunction with the moving least square method can calculate the SIFs from only nodal displacements obtained by the finite element analysis. We analyzed the SIFs of external circular interfacial cracks in jointed dissimilar anisotropic solids subjected to thermal load and showed the distributions of SIFs along the crack front. The distribution of stress and the crack opening displacement obtained by the asymptotic solution with the SIFs are compared with those obtained by the FEM with fine mesh. They are almost identical each other.

Green’s function for KI determination of axisymmetric elastic solids containing external circular crack

A new Green’s function is derived to determine the mode-I stress intensity factor for axisymmetric solids containing external circular crack. The formulated boundary integral equation is applied to a finite cylindrical bar with an external crack, and the obtained solution is compared with existing published results, indicating good agreement. The proposed method compared with the finite element method or the conventional application of the boundary element method provides the following main advantages: (a) it does not require discretization of the crack surface, (b) it does not require multi-region modeling and (c) it reduces the 3-D discretization of the solid to 1-D resulting in substantially reduced effort.

Mechanical Behavior and Failure Analysis of Prosthetic Retaining Screws after Long‐term Use In Vivo. Part 1: Characterization of Adhesive Wear and Structure of Retaining Screws

The general aim of this study and those presented in Parts 2-4 of this series was to characterize the structure, properties, wear, and fracture of prosthetic retaining screws in fixed detachable hybrid prostheses after long-term use in vivo. This part of the overall investigation addresses whether there are differences in thread wear between the screws closest to the fulcrum and those that are farthest from the fulcrum in fixed detachable hybrid prostheses. The total number of prosthetic retaining screws used in this study was 100 (10 new and 90 used). New screws (controls) from Nobel Biocare (NB) were divided into Group 1 (slotted) and Group 2 (hexed). Ninety used screws (in service 18-120 months) were retrieved from fixed detachable hybrid prostheses in 18 patients (5 screws from each patient, 60 from NB and 30 from Sterngold). The used screws were divided into 18 groups. Additionally, each group was subdivided into A and B categories. Category A contained the middle three prosthetic screws, which were considered the farthest screws from the fulcrum line. Category B contained the most posterior two screws, which were considered the screws closest to the fulcrum line. All 100 screws were subjected to thorough, nondestructive testing. Light and scanning electron microscopic examination of all used screws for each group revealed surface deterioration of the active profile of the screw threads consistent with adhesive wear. The observed thread profile deterioration ranged from mild to severe. The wear was aggressive enough to cause galling, which led to thinning of the threads and, in severe cases, to knife-edges at thread crests. In ten groups, the most anterior three screws exhibited more wear than the most posterior two screws. In addition to thread wear, severe plastic deformation was detected on the bottom part of each screw for three groups, and a long external longitudinal crack was detected in one screw of Group 2. The findings of this study and those presented in Parts 2-4 demonstrate that different retaining screws from the same manufacturer and/or from different manufacturers have different geometrical design, microstructures, major alloy constituents, and microhardness, and that these differences influence their preload and fractured load values. In this part of the overall investigation, the occurrence of galling as a result of wear involving prosthetic retaining screws appears to be an inevitable and unavoidable consequence of long-term use in vivo in fixed detachable hybrid prostheses regardless of the intended/original preload value. The galling rate is greater on the middle three screws compared to the most posterior two screws in fixed detachable hybrid prostheses. The wear pattern is consistent with an adhesive wear mechanism; however, this study does not provide enough data to support a definitive analysis.

Refined Dugdale plastic zones of an external circular crack

The refined Dugdale-type plastic zones ahead of an external circular crack, subjected to a uniform displacement at infinity, are evaluated both analytically and numerically. The analytical method utilizes potential theory in classical linear elasticity with emphasis on the contrast from the internal crack problem. A closed-form solution to the mixed boundary problem is obtained to predict the length of the plastic zone for a Tresca yield condition. The analytical solution is also used to benchmark the results obtained from the numerical method, which show good agreement. Through an iterative scheme, the numerical technique is able to estimate the size of crack tip plasticity zone, which is governed by the non-linear von Mises criterion. The relationships between the applied displacement and the length of the plastic zone are compared for the different yielding conditions. Computational modeling has demonstrated that the plastic constraint effect based on the true yield condition can significantly influence the load-bearing capacity. It is also discovered from the comparative study that the stress components predicted by the three different yield conditions may differ notably; however, the stress triaxiality in the ligament region has only small deviations. The proposed study may find applications in predicting the plastic flow in a circumferentially notched round bars under tension.

Super-heater tube failure due to overheating when using bagasse as fuel

A super-heater’s boiler tubes presented external longitudinal cracks. The tubes’ external surfaces presented a reddish-white layer consisting of paraffin chains: CH, functional groups: CO, NH and sulphur compounds. This brittle layer prevented heat transfer, thereby causing increased tube temperature. Creep led to failure due to long-term overheating. The steel tubes’ microstructure presented grain growth, cementite globulisation and intergranular cracks on the external surface. The foregoing observations support microstructure deterioration facilitated by the presence of unsuitable super-heater tube material when just using bagasse as fuel.

Thermal stress concentration factors for defects in plated-through-vias

Plated-through-vias (PTVs) are subject to thermal stress during soldering and in service. Plating and manufacturing defects in the PTV walls (barrels) can create stress concentrations that frequently become the sites of crack initiation during thermal fatigue. This is of growing concern as processing temperatures increase due to the use of lead-free solders, and boards become thicker generating increased stress as PTV aspect ratios rise, making it more difficult to achieve uniform plating thickness throughout the barrel. Finite element analysis (FEA) has been used to develop correlations that can be used to calculate the stress concentration factors (SCFs) for five typical defects as a function of various geometric parameters. In terms of their severity, the defects were ranked as: (1) rapid thickness reduction (SCF ⩽ 13), (2) occasional waviness (SCF ⩽ 4.6), (3) gradual thickness reduction (SCF ⩽ 4), (4) wicking (SCF ⩽ 4) and (5) waviness (SCF ⩽ 3.1). The SCF due to an internal pad and the influence of an external pad-barrel corner crack were also investigated. The maximum stress at the defect is found by multiplying the SCF by the von Mises stress at the mid-plane of the corresponding idealized PTV. The latter can be found using either an analytical model or correlations as a function of the aspect ratio and board-to-barrel thickness ratio that were developed using FEA.

Numerical and analytical study of severity of cracks in cylindrical and spherical shells

The present study deals with the severity of cracks in pressure equipments, where such defects are often involved. Our work is particularly concerned with the problem of cylindrical shells and also the little well-known problem of spherical shells, including all sorts of practical defects, namely axisymmetric or semi-elliptic, both internal and external cracks. The stress intensity factor in the linear elastic domain and the J integral in the elastoplastic range are performed using the finite element method and compared to the results provided by the application of the semi-analytical A16 or R6 simplified criteria, depending on a limit load calculation. The nocivity of the defects depends on the crack shape and size and other structural geometrical parameters. Use is made of a polynomial decomposition of the stress field in the vicinity of the crack in order to cover all industrial loadings. All the numerical results, for a wide range of shell and crack geometries, are depicted using appropriate tables and curves in order to check the fracture criteria more easily.

Stressed state of a cylinder with external circular crack under dynamic torsion

We have proposed a combined analytical and experimental method for the determination of dynamic stress intensity factors in impact torsion tests of cylindrical specimens with an external circular crack. We have obtained simple analytical relations for finding dynamic stress intensity factors, which contain parameters determined experimentally. The results obtained with the use of these relations are in good agreement with those based on the finite element method. We have carried out an electron-fractographic analysis of the fracture surfaces of specimens and have described the characteristic mechanisms of fracture under high-rate torsion of cylindrical specimens.

Remaining life assessment of welded pipes containing cracks

The presence of flaws, their size and location in the welded region affects the safe service life of pressure pipes operating at elevated temperature. A remaining life assessment was required to determine the probable remaining safe life of pressure pipes in a high-temperature steam distribution system in which crack-like defects had been identified in many welds. The crack-like defects indicated by NDE lacked the required information to fully identify their locations within the pipe wall. The effect of not knowing complete details of the location of the identified cracks was studied by considering a 360° circumferential crack with initial radial dimension a 0. The crack positions evaluated were: an internal surface crack, an external surface crack, and embedded cracks at various distances from the internal wall of the pipe. Crack growth was modeled using time-dependent fracture mechanics and a newly developed computer code.

The elastic field of general-shape 3-D cracks

We extend here the Bilby-Eshelby approach of 2-D crack representation with dislocation pileups to treat 3-dimensional cracks of general geometry. Cracks of any specified external bounding 3-D contour under general loading conditions are represented by sets of parametric Somigliana loops that satisfy total (interaction, self, and external) force equilibrium. Loop positions are solved by using a time integration scheme till equilibrium is achieved. The local Burgers vector is suitably adjusted to be proportional to the local applied surface traction on the crack. The developed method is computationally advantageous, since accurate crack stress fields are obtained with very few concentric parametric loops that adjust to the external crack shape and the local force conditions. The method is tested against known elasticity solutions for 3-D cracks and found to be convergent with an increase in the number of pileup dislocation loops. The method is applied to the determination of the stress field around a 3-D Griffith crack under general loading and a grain boundary crack before and after branching.

증기발생기 전열관에 존재하는 표면균열의 한계하중 평가

Operating experience of steam generators has shown that cracks of various morphology frequently occur in the steam generator tubes. These cracked tubes can stay in service if it is proved that the tubes have sufficient safety margin to preclude the risk of burst and leak. Therefore, integrity assessment using exact limit load solutions is very important for safe operation of the steam generators. This paper provides global and local limit load solutions for surface cracks in the steam generator tubes. Such solutions are developed based on three-dimensional (3-D) finite element analyses assuming elastic-perfectly plastic material behavior. For the crack location, both axial and circumferential surface cracks, and for each case, both external and internal cracks are considered. The resulting global and local limit load solutions are given in polynomial forms, and thus can be simply used in practical integrity assessment of the steam generator tubes.

Characterization of the Failure and the Effect of Carbon Fiber Reinforced Composites on the Cracking in Cement Constructions I-Tensile Characteristics

Recently, fiber reinforced plastics have found applications in civil engineering. Owing to their mechanical properties, these materials have replaced steel and steel plates for external crack repairs in deteriorated structures. Fiber reinforced plastic sheets can be fixed to the structural parts in need of repair, using suitable adhesives. In this article, a new clamping system is introduced that simulates the actual cracking effect. Carbon fabric and its reinforced epoxy laminated composite material are used to join together two parts of a sand-cement mixture by an adhesive at three different gage lengths. Upon the effect of cracking, the performance of the adhesive joint is found to act differently with each material. The three-layer laminated composite is found to act better than the fabric. Each gage length shows a different joint strength.

Comparison of semi-elliptical cracks in cylinders with a thickness transition and in a straight cylinders – Elastic–plastic behaviour

This paper presents a study of a circumferential external semi-elliptical crack in a cylinder with a thickness transition. Crack harmfulness is compared to the harmfulness of a similar crack in a straight cylinder, on the basis of J-integral calculations. Loads considered are pure tensile stress and bending moment. A numerical analysis is performed considering elastic plastic behaviour of material. A crack mesh was designed for 3D models. The results show that the cylinder with a thickness transition is more vulnerable to the defect. A simple method for J calculation at the deepest point of the crack in the transition zone is also proposed.

Finite element analysis of the effects of radial expansion of corroded reinforcement

A finite element (FE) model of the effects of corroding reinforcement on the surrounding concrete was validated against the results of simulated corrosion tests in which internal pressure was applied to holes cast in concrete. The model was then used to explore the effects of bar radial expansion, due to the formation of corrosion products, on the cracking of cover concrete. The predictions were compared with test results from reinforced concrete accelerated corrosion specimens. The aim of the analytical investigation was to reveal the mechanism for the development of concrete cracking due to the corrosion of reinforcement. The three-dimensional physical specimens were idealised as two-dimensional analytical models under a plane strain assumption. Corrosion of reinforcement was modelled as either an internal pressure or a radial expansion to analyse the results of simulated and accelerated corrosion specimens, respectively. The FE analytical results indicate that the radial expansion of corroded reinforcement causes concrete cover to crack in four different stages: internal cracking, external cracking, penetration cracking and ultimate-cracking. It was also found that the FE analytical results could be used to explain qualitatively the experimentally determined relationship between amount of corrosion for concrete cracking and ratio of concrete cover to bar diameter, as well as that between reinforcement bond strength and amount of corrosion.