Analytical model for time to cover cracking in RC structures due to rebar corrosion

The structural degradation of concrete structures due to reinforcement corrosion is a major worldwide problem. Reinforcement corrosion causes a volume increase due to the oxidation of metallic iron, which is mainly responsible for exerting the expansive radial pressure at the steel–concrete interface and development of hoop tensile stresses in the surrounding concrete. Cracking occurs, once the maximum hoop tensile stress exceeds the tensile strength of the concrete. The cracking begins at the steel–concrete interface and propagates outwards and eventually results in the thorough cracking of the cover concrete and this would indicate the loss of service life for the corrosion affected structures. An analytical model is proposed to predict the time required for cover cracking and the weight loss of reinforcing bar in corrosion affected reinforced concrete structures. The modelling aspects of the residual strength of cracked concrete and the stiffness contribution from the combination of reinforcement and expansive corrosion products have also been incorporated in the model. The problem is modeled as a boundary value problem and the governing equations are expressed in terms of the radial displacement. The analytical solutions are presented considering a simple two-zone model for the cover concrete, viz. cracked or uncracked. Reasonable estimation of the various parameters in the model related to the composition and properties of expansive corrosion products based on the available published experimental data has also been discussed. The performance of the proposed corrosion cracking model is then investigated through its ability to reproduce available experimental trends. Reasonably good agreement between experimental results and the analytical predictions has been obtained. It has also been found that tensile strength and initial tangent modulus of cover concrete, annual mean corrosion rate and modulus of elasticity of reinforcement plus corrosion products combined significantly influence predicted time to cover cracking. The analytical predictions of the proposed model have also been found to be in line with those of the other reported published data.     

The effect of crack location and maximum stress position on the failure of a cracked piping system

The failure of a circumferentially cracked stainless steel piping system can be predicted by assuming that failure conforms to a net-section stress criterion, using as input an appropriate value for the critical net-section stress together with a knowledge of the anticipated loadings. The usual procedure is to calculate the stress acting on the cracked section via a purely elastic analysis based on the piping system being uncracked. However (a) the piping is built-in at the system ends into a larger component, and (b) the onset of crack extension requires some plastic deformation. Consequently, use of the net-section stress approach to predict the onset of crack extension, can give overly conservative failure predictions. Earlier work by the author has quantified the extent of this conservatism, and has shown how it depends on the material ductility and the geometry of the cracked section. It has also been demonstrated that the extent of conservatism depends on the elastic flexibility of the system, and in particular on the location of the cracked section within the system. The present paper extends these earlier studies, and shows that the location for which crack extension is favoured is not necessarily that location where the stress (calculated on the basis of an uncracked system analysis) is a maximum, as is implicitly assumed when the net-section stress approach is used.     

Dynamic behaviour of anchors in cracked and uncracked concrete: a progress report

In early 1993, the US Nuclear Regulatory Commission began a research program at The University of Texas at Austin, dealing with the dynamic behavior of anchors in cracked and uncracked concrete. In this paper, the progress of that research program is reviewed. The test program is summarized, and work performed to date is reviewed, with emphasis on the dynamic and static behavior of single tensile anchors in uncracked concrete. General conclusions from that work are discussed, and future plans are presented.     

Monitoring of inside surface crack growth by strain measurement of the outside surface: A feasibility study

Cracks detected by in-service inspections are not always removed when they are judged to be not hazardous according to fitness-for-service evaluations. In order to secure the integrity of the cracked components, it is important to confirm that the cracks do not grow notably beyond the growth prediction conducted for the judgement. However, due to the limitation of accuracy of size determination by the current inspection techniques such as ultrasonic testing, it is difficult to know how much the cracks have grown since their previous measurement. In this study, feasibility of a crack growth monitoring method (outside strain monitoring method) was evaluated by finite element analyses and experiments. When a pipe deforms elastically due to internal pressure, the strain at its outside surface increases. The magnitude of strain near the crack differs from that at an uncracked portion, and the difference depends on the crack size. Elastic finite element analyses were performed for cracked pipes under internal pressure for various crack sizes. It was shown that, by measuring the change in strain at the outside surface of the cracked pipe, the crack size and how much the crack grew can be identified. In the experiment, cracked pipes were subjected to static internal pressure and strains for eight cracks of different sizes were measured. It was revealed that the maximum error was 0.44 mm for the estimation of crack depth of 4 mm and 0.28 mm for the estimation of 1 mm crack growth in the depth direction.     

Analysis and application of prestressed concrete reactor vessels for LMFBR containment

An analytical model of a prestressed concrete reactor vessel (PCRV) for LMFBR and the associated finite element computer code, involving an explicit time integration procedure, is described. The model is axisymmetric and includes simulations of the tensile cracking of concrete, the reinforcement, and a prestressing capability. The tensile cracking of concrete and the steel reinforcement are both modeled as continuously distributed within the finite element. The stresses in the reinforcement and concrete are computed separately and combined to give an overall stress state of the composite material. The reinformcement is assumed to be elastic, perfectly-plastic; the concrete is taken to be elastic, with tensile and compressive stress limits. Cracking of concrete is based on the criterion of maximum principal stress; a crack is assumed to form normal to the direction of the maximum principal stress. Attention is also given to the fact that cracks do not form instantaneously, but develop gradually. Thus, after crack initiation the normal stress is reduced to zero gradually as a function of time. Residual shear resistance of cracks due to aggregate interlock is also taken into account. An existing crack is permitted to close. Prestressing of the PCRV is modeled by special structural members which represent an averaged prestressing layer equivalent to an axisymmetric shell. The internal prestressing members are superimposed over the reinforced concrete body of the PCRV; they are permitted to stretch and slide in a predetermined path, simulating the actual tendons.The validity of the code is examined by comparison with experimental data. Both static and dynamic data are compared with code predictions, and the agreement is satisfactory. A preliminary design has been developed for both pool and loop-type PCRVs. The code was applied to the analysis of these designs. This analysis reveals that the critical locations in such a design would be the head cover and the junction between the cover and the vessel wall and indicates the pattern of crack development. The results show that the development of a design adequate for current HCDA loads is quite feasible for pool-type or loop-type PCRVs.     

Response of reinforced concrete structures to macrocell corrosion of reinforcements. Part I: Before propagation of microcracks via an analytical approach

Assessment of the macrocell corrosion which deteriorates reinforced concrete (RC) structures have attracted the attention of many researchers during recent years. In this type of rebar corrosion, the reduction in cross-section of the rebar is significantly accelerated due to the large ratio of the cathode's area to the anode's area. In order to examine the problem, an analytical solution is proposed for prediction of the response of the RC structure from the time of steel depassivation to the stage just prior to the onset of microcrack propagation. To this end, a circular cylindrical RC member under axisymmetric macrocell corrosion of the reinforcement is considered. Both cases of the symmetric and asymmetric rebar corrosion along the length of the anode zone are studied. According to the experimentally observed data, corrosion products are modeled as a thin layer with a nonlinear stress–strain relation. The exact expressions of the elastic fields associated with the steel, and concrete media are obtained using Love's potential function. By imposing the boundary conditions, the resulting set of nonlinear equations are solved in each time step by Newton's method. The effects of the key parameters which have dominating role in the time of the onset of concrete cracking and maximum radial stress field of the concrete have been examined.     

Random cyclic stress–strain responses of a stainless steel pipe-weld metal II — a modeling

This paper pays special attention to an issue that there is a significant scatter of the stress–strain responses of a nuclear engineering material, 1Cr18Ni9Ti stainless steel pipe-weld metal. Efforts are made to reveal the random fatigue damage character by fracture surface observations and to model the random responses by introducing probability-based stress–strain curves of Ramberg–Osgood relation and its modified form. Results reveal that the fatigue damage is subjected to, 3-D interacting and involved microcracks. The three stages, namely microstructural short cracks (MSC), physical short cracks (PSC) and long cracks (LC) subdivided by Miller and de los Rios, can give a good characterization of the damage process. Both micro- and macro-behaviour of the material have the character of three stages. The 3-D effects are strong in the MSC stage, tend to a gradual decrease in the PSC stage, and then show saturation after going to the LC stage. Intrinsic causes of the random behaviour are the difference and evolution of the microstructural conditions ahead of the dominant crack tips. The ‘effectively short fatigue crack criterion’ introduced by Zhao et al. in observing the material surface short crack behaviour could facilitate an understanding of the mechanism of interaction and evolution. Based on the previous obtained appropriate assumed distribution, normal model, for the cyclic stress amplitude, the probability-based curves are approximated by the mean value and standard deviation cyclic stress–strain curves. Then, fatigue analysis at arbitrarily given reliability can be conveniently made according to the normal distribution function. To estimate these curves, a maximum likelihood method is developed. The analysis reveals that the curves could give a good modeling of the random responses of material.     

A scheme for finite element analysis of mode I and mixed mode stable crack growth and a case study with AISI 4340 steel

A new scheme for elastic–plastic finite element analysis has been proposed for the study of stable crack growth (SCG) from initiation to instability in both mode I and mixed modes (I and II). The scheme is based on node-release technique and helps to determine the variation of fracture load with crack extension without requiring much computer storage and time. The scheme permits predictions of load variation with load line displacement (LLD), maximum fracture load, crack tip current plastic zone and crack edge profile. In the analysis the condition for crack extension at every stage of the SCG is considered to be governed by CTOA/COD reaching a critical value. The scheme of analysis is different from the ones proposed by earlier investigators. The whole SCG is analysed in a few stages using the ANSYS software and a single discretization. Element arrangement in the discretization is decided from the very beginning; it has a capability of accommodating changes in boundary conditions arising out of crack extension in the later stages. Each stage is analysed afresh ignoring state of stress–strain reached at a material point at the end of the previous stage. Case studies on both mode I and mixed mode presented considering AISI 4340 steel, which is widely used in nuclear power industry, indicate that the SCG through it can be characterized in terms of a single COD or CTOA. Predictions for the initiation and maximum fracture loads in both the cases compare very closely with the experimental data reported. The results presented also include the value of critical COD/CTOA (0.035 mm/0.0875 rad) characterizing the SCG through the steel and show that the initiation load is not significantly affected by crack tip radius up to 0.05 mm.     

Preliminary results of post-irradiation examinations on LiSoR-2 test section

Liquid-solid reaction under irradiation (LiSoR) experiments are aimed at understanding the effects of liquid lead-bismuth eutectic (LBE) corrosion and embrittlement under irradiation on structural materials, which is one of the key items of the materials R&D for the future accelerator-driven system (ADS). The LiSoR setup is basically a LBE loop with a test section irradiated with 72 MeV protons. The second irradiation was conducted for about 34 h and terminated after a leakage of LBE was detected. Post-irradiation examinations (PIE) are being performed on both the tube and tensile specimen in the test section. Optical microscopy, scanning electron microscopy, transmission electron microscopy and microhardness tests have been completed. The results show that a crack formed in the irradiation zone of the tube. In the material in the irradiation zones of both the tube and the tensile specimen dislocation cell structure is well developed, which indicates heavy deformation due to thermal fatigue. The crack should start at the inner surface and propagate to the outer surface. The fracture surfaces of the crack are dominated by a brittle cleavage fracture mode. However, on the surfaces of the tensile specimen, no microcracks are observed.     

氧化物夹杂与Ni-Cr-Mo-V钢多层焊缝低温冲击韧性变化规律的关系

测试了反应堆压力容器用Ni-Cr-Mo-V钢焊缝的冲击韧性,实验结果表明,当实验温度较低时,同一实验温度下沿盖面焊到焊根方向不同层焊缝样品的冲击吸收能呈下降趋势。通过低温实验样品断口观察到韧窝底部、起裂源、解离断刻面裂纹源存在直径为0.3～2.0 μm的球形氧化物夹杂,导致试样在变形过程中氧化物夹杂与基体分离形成微裂纹,并发展为试样的韧窝、起裂源和解离断刻面裂纹源,由此推断氧化物夹杂是造成焊缝低温失效的主要原因。同时氧化物夹杂的数量沿盖面焊到焊根方向逐渐增多,使得微裂纹形核率逐渐增加,造成焊缝低温冲击韧性沿盖面焊到焊根方向逐渐变差。     

Chemically assisted crack nucleation in zircaloy

Stress corrosion cracking models (proposed to explain fuel rod failures) generally address crack propagation and cladding rupture, but frequently neglect the necessary nucleation stage for microcracks small enough to violate fracture mechanics continuum requirements. Intergranular microcrack nucleation was modeled with diffusion-controlled grain-boundary cavitation concepts, including the effects of metal embrittlement by iodine species. Computed microcrack nucleation times and strains agree with experimental observation, but the predicted grain-boundary cavities are so small that detection may be difficult. Without a protective oxide film, intergranular microcracks can nucleate within 30 s at even low stresses when the embrittler concentration exceeds a threshold value. Indications were found that intergranular microcrack nucleation may be caused by combined corrosive and embrittlement phenomena.     

Special features of steam–gas flow through a crack in the protective envelope of a nuclear power plant

Experimental data on the escape of steam and liquid drops with the outflow of a steam–air mixture through a model of a crack in a concrete protective envelope are presented. The experiments are performed using cold and heated concrete assemblies. Complete condensation of the steam on the surface of a crack occurs at relatively low temperatures of the concrete assembly. As the concrete assembly is heated, drops appear in the gas flow at the exit.Translated from Atomnaya Énergiya, Vol. 97, No. 5, pp. 333–338, November, 2004.     

The J integral evaluation of a nozzle corner crack under thermal transient loading condition

This paper presents the results of the evaluation of the three dimensional J integral of a nozzle corner crack which is initiated by fatigue under thermal transient loading conditions of a BWR type reactor vessel. Analyses are carried out by using the finite element method in the following two cases. One case consideres the effect of the stainless steel cladding deposited over the inside surface of the reactor vessel, and the other neglects it. In both cases, the extended J integral concept, called integral, is used to obtain the path independent J value in the thermal stress fields.By changing the shapes and the dimensions of the crack, some elastic analyses are carried out in the two dimensional space. The effects of the cladding are studied qualitatively, and the integrals are compared with the critical J value, and discussed.Three dimensional values along the three dimensional crack front are evaluated for the embedded crack. The results are compared with those for two dimensional analysis.The nozzle corner crack is treated under thermal transient condition and distributions of values, and their change with time is obtained. The shapes and dimensions are changed by the assumption that the crack growth occurs at the point where the vector has its maximum, and the three dimensional shape of the propagating crack is estimated.     

Correlation between characteristics of fracture process zone and tension-softening properties of concrete

The microcracking properties of concrete are studied by means of the three-dimensional acoustic emission technique in order to discusse the phases of the fracture process zone of concrete. It is revealed that the length of the fracture process zone ahead of the notch tip seems to be independent of the maximum aggregate size but the width is obviously influenced by this factor.The tension-softening properties are analysed as an inverse problem. Among the four parameters defining a bilinear tension-softening diagram, the critical crack width is most influenced by the heterogeneity. The numerical results are correlated with the phases of the fracture process zone. The size dependence of the fracture energy of concrete is also discussed on the basis of the characteristics of the fracture process zone and an empirical formula is proposed to describe the size dependence.     

Oxidation behaviour of zirconium alloys and their precipitates – A mechanistic study

The precipitate oxidation behaviour of binary zirconium alloys containing 1 wt.% Fe, Ni, Cr or 0.6 wt.% Nb was characterised in TEM on FIB prepared transverse sections of the oxide and reported in previous studies [1], [2]. In the present study the following alloys: Zr1%Cu, Zr0.5%Cu0.5%Mo and pure Zr are analysed to add to the available information. In all cases, the observed precipitate oxidation behaviour in the oxide close to the metal-oxide interface could be described either with delayed oxidation with respect to the matrix or simultaneous oxidation as the surrounding zirconium matrix. Attempt was made to explain these observations, with different parameters such as precipitate size and structure, composition and thermodynamic properties. It was concluded that the thermodynamics with the new approach presented could explain most precisely their behaviour, considering the precipitate stoichiometry and the free energy of oxidation of the constituting elements.The surface topography of the oxidised materials, as well as the microstructure of the oxide presenting microcracks have been examined. A systematic presence of microcracks above the precipitates exhibiting delayed oxidation has been found; the height of these crack calculated using the Pilling–Bedworth ratios of different phases present, can explain their origin. The protrusions at the surface in the case of materials containing large precipitates can be unambiguously correlated to the presence of these latter, and the height can be correlated to the Pilling–Bedworth ratios of the phases present as well as the diffusion of the alloying elements to the surface and their subsequent oxidation. This latter behaviour was much more considerable in the case of Fe and Cu with Fe showing systematically diffusion to the outer surface.     

Stress intensity factors of two bonded half-plane problem with a point heat source

The two-dimensional thermoelastic crack problem of two bonded dissimilar media with a point heat source is considered in this paper. Based on the complex variable theory and the method of analytical continuation, the problem is formulated by two stress functions and a temperature function for each material medium which are enforced to satisfy the interface condition. Furthermore, the singular integral equations are derived by taking some density functions along the crack border in a way that the traction-free condition is satisfied on the crack surface. Numerical results for both half-plane and two bonded half-plane problems associated with a curved crack or a line crack under a point heat source are presented and provided in graphic form.     

Microstructure-mechanical property relations in HT-9

In this study we have investigated the possible relationships between microstructural features and cleavage fracture behavior of HT-9 specimens heat treated to twenty-five conditions. Fractographic analyses, including direct observation of fracture surfaces as well as subsurface examination, suggest that cleavage crack initiation is associated with the fracture of large carbides, primarily at prior austenite grain (PAG) boundaries. These microcracks are inhibited from propagating across lath packet or PAG boundaries, where ductile tearing occurs. Carbide size and the extent of ductile tearing can be used to rationalize the observed trends in cleavage fracture parameters.     

Air–steam leakage through cracks in concrete walls

In the context of a severe accident in a PWR nuclear plant, the evaluation of the leakage through the containment wall remains a key point of the safety analysis. Here we calculate the leakage of an air steam mixture through a traversing crack taking into account condensation. A 40 h test has been performed on a representative concrete slab with measurements of crack openings and flow rates. The CAST3M code enables us to simulate this test by making thermo-mechanical calculations and calculation of the leakage flow rate. Thermo-mechanical calculations provide data needed by the leakage calculations which are not measurable in the experiment. These are the internal crack profiles (variation of the opening with the curvilinear coordinate of the crack inside the concrete slab). Thermo-mechanical calculations are difficult to perform because boundary conditions of the test are complicated. Leakage calculations are performed with various hypotheses for the internal cracks profiles. A coefficient is applied on the friction factor to take into account additional complexity of the crack geometry.     

Thermodynamic model of helium and hydrogen co-implanted silicon surface layer splitting

A thermodynamic model of the evolution of microcracks in silicon caused by helium and hydrogen co-implantation during annealing was studied. The crack growth rate relies on the amount of helium atoms and hydrogen molecules present. Here, the crack radius was studied as a function of annealing time and temperature, and compared with experimental results. The mean crack radius was found to be proportional to the annealing temperature and the helium and hydrogen implanted fluence. The gas desorption should be considered during annealing process.