M. K. Samal

Estimation of transverse tensile behavior of Zircaloy pressure tubes using ring-tensile test and finite element analysis

Determination of transverse mechanical properties from the ring type of specimens directly machined from the nuclear reactor pressure tubes is not straightforward. It is due to the presence of combined membrane as well as bending stresses arising in the loaded condition because of the curvature of the specimen. These tubes are manufactured through a complicated process of pilgering and heat treatment and hence, the transverse properties need to be determined in the as-manufactured condition. It may not also be possible to machine small miniaturized specimen in the circumferential direction especially in the irradiated condition. In this work, we have performed ring-tensile tests on the un-irradiated ring tensile specimen using two split semi-cylindrical mandrels as the loading device. A three-dimensional finite element analysis was performed in order to determine the material true stress–strain curve by comparing experimental load–displacement data with those predicted by finite element analysis. In order to validate the methodology, miniaturized tensile specimens were machined from these tubes and tested. It was observed that the stress–strain data as obtained from ring tensile specimen could describe the load–displacement curve of the miniaturized flat tensile specimen very well. However, it was noted that the engineering stress–strain as directly obtained from the experimental load–displacement curves of the ring tensile tests were very different from that of the miniaturized specimen. This important aspect has been resolved in this work through the use of an innovative type of 3-piece loading mandrel.

Investigation of Deformation Behavior of Ring-Tensile Specimens Machined from Pressure Tubes of Indian PHWR

Specimens machined in the form of circular rings directly from the nuclear reactor pressure tubes and tested in a ring-tension test-setup offer great simplicity in evaluating the transverse mechanical properties of the as-manufactured as well as those of the service-exposed tubes. However, the state of stress in the specimen cross-section is not purely uni-axial due to the effect of bending and the presence of lateral pressure due to the loading mandrel. This requires the use of 3-D finite element (FE) analysis for simulation of deformation behavior of the specimens in the ring-tension test-setup. In this work, we have analyzed the deformation behavior of ring-tension specimens machined from two different types of zirconium alloy pressure tubes as used in the Indian pressurized heavy water reactors. The effect of geometry of the loading mandrel (i.e., 2-piece vs. 3-piece type of mandrel) on the load-deformation behavior of the test-setup has been studied. It was observed that the values of maximum load as well as the deformation behavior in the post-necking region differ significantly when only the geometry of the loading mandrel is changed keeping all the other parameters same. FE analysis has been able to correctly predict these variations as it takes into account of the effect of geometry, material properties as well the interaction between the mandrel and the specimen. Hence, the use of FE method is essential in the inverse analysis procedure where the material properties can be determined from these complex test-setups.

A mathematical model in three-dimensional piezoelectric continuum to predict non-linear responses of piezoceramic materials

Abstract It has been experimentally observed that the piezoceramic materials exhibit different types of non-linearities under different combinations of electrical and mechanical fields. When excited near resonance in the presence of weak electric fields, they exhibit typical non-linearities similar to a Duffing oscillator such as jump phenomena and the presence of superharmonics in the response spectra. In this work, these non-linearities have been modelled for a generalized three-dimensional piezoelectric continuum using higher-order quadratic and cubic terms in the electric enthalpy density function and the virtual work. The identification of the parameters of the model requires a closed form solution for non-linear response of a simplified geometry. A simple proportional damping formulation has been used in the model. Experiments have been conducted on rectangular and cylindrical geometries of piezoceramic PIC 181 at different magnitudes of applied electric fields and results have been compared with those of simulation.

A study on ductile fracture initiation in the PHT piping material of an Indian PHWR using local approach

Abstract The ductile fracture phenomenon is a local mechanism, which consists of nucleation, growth and coalescence of microscopic voids. These microscopic voids are generally formed around the second phase particles because of the debonding of these particles from the parent matrix or the cracking of these particles themselves. In the present work, the ductile fracture of primary heat transport (PHT) system piping material of an Indian pressurised heavy water reactor (PHWR) was analysed using different models of local approach. Such local approaches use micromechanical models to predict crack initiation and stable crack growth. Two different types of models are used. The first one is based on the critical cavity growth (Rice and Traceys cavity growth model and Budiansky and coworkers model). The other model is based on the combined effect of damage and yielding (Tai and Yangs and modified Tai and Yangs model). An in-house Elasto-Plastic finite element code thesis was modified and used for the analysis of the notched tensile specimens. In addition, the notched round tensile specimens were used to determine the true stress–strain curve. The fracture strains of the different specimens were determined from the experiment with some modifications. By integrating the cavity growth equations of the respective models up to the fracture strain, the critical values of the parameters were determined. The effect of hydrostatic stress on the critical parameters was studied by varying the notch root radius of the specimens. It was observed that the critical value of Rice and Traceys parameter is a weak function of stress triaxiality whereas critical parameters of other models showed more dependency on the level of triaxiality. Especially Budiansky and coworkers model showed maximum variation of the parameter with respect to the notch root radius.

A Practical Approach to Evaluate Stress-Strain Behavior of Remotely Handled Pressure Tubes of Nuclear Reactors Using Ring Tension Test

Determination of transverse mechanical properties of nuclear reactor pressure tubes is important to perform integrity assessment of these components, especially for those which have been subjected to extended duration of reactor operation. Machining of standard tensile specimens is difficult in case the specimens are to be obtained from these thin tubular components. However, the more practicable option would be to fabricate the ring tensile type of specimens by directly machining them from the tube as it is a less cumbersome option in comparison to that of machining of the miniature plate tensile specimens especially when the component has been discharged from the nuclear reactor and are to be handled remotely due to activity. But, adopting this approach requires certain specific standardization work to be done to make the technique fully acceptable, adaptable and reliable when compared to the conventional techniques.In this work, we have developed a practical approach to evaluate the transverse mechanical properties and the stress–strain behavior of tubular components using ring tensile test. Different types of mandrel design and gauge length orientations of the specimens with respect to loading axis have been explored and the dependence of the results on the above parameters has been discussed. Two different types of Zirconium based alloys as used in Indian nuclear reactors have been tested with this technique and the material stress–strain behavior have been evaluated. Finally, the advantages of this method to evaluate the transverse mechanical properties of remotely-operated tubular components have been highlighted and use of appropriate loading and mandrel geometry for the ring tensile test have been recommended. The paper elucidates the methodology followed in validating the ring tensile test results in order to make the test suitable for the estimation of the irradiation-induced alteration in mechanical properties of nuclear reactor pressure tubes.

Evaluation of Material JR and Fracture Toughness Transition Curves using Micro‐Mechanical Modeling

Local approach has been used to compute a) Jinitiation and JR curves at different temperatures and b) fracture toughness transition curves at different probability of failure. The material under investigation is the Reactor Pressure Vessel Steel 22NiMoCr37. Ductile fracture has been analyzed using Gurson material constitutive model and probability of cleavage failure is calculated using Beremin’s model. A variation of Gurson parameter q2 near crack tip region as a function of charpy energy is suggested to obtain Jinitiation as well as complete JR curve accurately at different metal temperatures.

An atomistic modelling and statistical analysis study of crack–void interaction in Aluminum

Abstract The interaction between a brittle crack and pre-existing void in front of the crack tip was studied in the realm of molecular dynamics simulations at the nanoscale in face centred cubic Al within the framework of embedded-atom method. The results provide corroborative evidence of the fact that presence of a void in front of a running crack deters further crack growth. By performing an extensive series of simulations with different void sizes and crack-void distances coupled with statistical analysis, it has been found that (1) major role of voids is to decrease the fracture stress with increasing void size, in addition to slight increase in strain at which the crack growth occurs and the consequent strain to fracture, (2) fracture stress for a constant void size follows a sinusoidal distribution by varying the crack-void distance and (3) it is the void size that is most crucial in dictating the fracture properties of the material, rather than the void placement.

Evaluation of Fracture Resistance Behavior of Zircaloy Fuel Clad Tubes of Indian PHWRs Using Experiments on Ring Specimens and Continuum Damage Mechanics Models

AbstractContinuum damage mechanics models are very popular in prediction of crack growth and fracture resistance behavior of low-alloy ferritic and austenitic stainless steel components of nuclear reactors with various postulated flaws under different loading conditions. However, literature regarding the application of the above models for prediction of fracture behavior of Zirconium alloys, which are used for manufacture of fuel-clad and pressure tubes etc., are very limited. These models are very useful for designers and safety analysts as the parameters of the models are truly material properties and are transferable from the specimen to the component level. In this work, the nonlocal version of the Rousselier’s damage model was used to predict the fracture resistance behavior of double-edged-notched-tensile specimens made from Zircaloy-4 material. Initially, the micro-mechanical parameters were determined from the testing of ring-type specimens. Subsequently, these parameters were used in finite element analysis of the double-edged-notched-tensile specimen in order to predict the crack growth behavior and the crack path under applied displacement-controlled loading conditions. The fracture resistance behavior obtained in terms of J-R curve was also compared with the corresponding J-R curves of an axially-cracked pin-loading-tension specimen. The results were also compared with similar data from literature wherever possible. From the above results, it can be concluded that the nonlocal Rousselier’s damage model is a suitable tool for prediction of accurate fracture resistance behavior of various Zirconium alloy components in the nuclear reactors in order to ensure structural integrity of the above components in various postulated accidental scenarios.

Experimental and Numerical Investigation of a Ring Tensile Test for Evaluation of Mechanical and Fracture Properties of Thin-Walled Fuel-Clad Tubes

Thin-walled fuel clad tubes of Zircaloy-4 material are used in nuclear reactors to hold fuel pellets. The design and safety analysis of these tubes requires estimation of the transverse mechanical and fracture properties at un-irradiated as well as service-exposed conditions. These thin-walled tubes are subjected to radial loading conditions due to expansion of fuel pellets during reactor operation. This loading condition exhibits the presence of combined tensile as well as bending stresses due to the curvature of the specimen and, as such, the tensile properties cannot be directly evaluated from the experiments on ring tensile specimens. In this work, ring tension tests were carried out on specimens machined from fuel-clad tubes. Both the specimen and the loading mandrel were modeled using the finite element (FE) method to evaluate the load–displacement behavior of the test. Rousseliers micro-mechanical model for ductile fracture was applied in order to simulate the crack growth in these specimens. The method was also validated by testing a ring–tension specimen (machined from alloy steel material) of similar dimension as that of the Zircaloy fuel pin specimen and then comparing the stress–strain curve with that of a standard round tensile specimen. The micro-mechanical parameters of the damage model were used to simulate the crack propagation in a standard double-edged notched tensile (DENT) specimen. The J–R curve of the DENT specimen has also been compared with that of a cracked pin–loading–tension (PLT) specimen. It was observed that the parameters of the Rousseliers model are able to predict the fracture resistance behavior of cracked fuel pins specimens satisfactorily, which have been obtained through a combined experiment and FE analysis of the ring tensile specimens. Thus, this method can be used to determine the material properties of irradiated and service-aged fuel pins as obtained from the nuclear reactors after different periods of reactor operation.

Design Aspects of a Ring Tension Test Setup and Evaluation of Transverse Material Stress-Strain Curve of Tubular Components Using FE Analysis

Ring tensile specimens are often used to determine the transverse properties of tubular components due to ease in fabrication and handling. Due to the presence of combined tension, bending, lateral pressure, and friction stresses in the ring tension test setup, it is essential to employ a computational tool in order to evaluate the transverse mechanical properties of these tubes accurately. On the other hand, choice of suitable loading mandrel and loading geometry may facilitate estimation of mechanical properties directly from the tests. In this work, the effect of various types of mandrel design and loading geometries on the load-displacement response of a ring specimen were studied. Finite element analysis with material, geometric, and contact nonlinearities were used in order to simulate the plastic deformation behavior of the specimen in ring tension setup and a novel algorithm was employed to extract the material stress-strain curve from experimental data. In addition, it was observed that a 3-piece mandrel with gage length oriented perpendicular to loading axis produced data which closely fits with the results from finite element analysis.