B.K. Dutta

Experimental and analytical study of three point bend specimen and throughwall circumferentially cracked straight pipe

Abstract Transferability of the specimen J–R/J–T curve to the component level is an important issue in the field of fracture mechanics. Towards this goal, fracture experiments have been carried out on three point bend (TPB) specimen and throughwall circumferentially cracked straight pipe of 219 and 406xa0mm outer diameter under four point bending load. The pipe material is SA333Gr6 and TPB specimens are machined from pipes. The image processing technique has been used to measure the crack growth and crack opening displacement in pipes. Component J–R curves have been generated from the load-deflection and load-crack growth data of pipe fracture experiments. These are compared with the TPB specimen J–R curves. Power law and second order polynomial fitting are done on the specimen and component J–R curves and J–T curves are generated. Specimen and component J–T curves are compared. Maximum moments in the pipe fracture experiments are also compared with the critical moments predicted by the ‘G factor’, ‘Z factor’ and limit approach.

Transferability of specimen J-R curve to straight pipes with throughwall circumferential flaws

Abstract The stress triaxiality is an important parameter in explaining the geometry dependence of J–R curves. By comparing the stress triaxiality across the ligament of a specimen and a cracked component, it is possible to assess whether the cracked component exhibits similar fracture behaviour to the specimen. In the present investigation, fracture experiments have been carried out on throughwall circumferentially cracked 8-in. diameter pipes under four point bending load and three point bend bar (TPBB) specimens machined from the same pipe. Subsequently, 3-D elastic–plastic finite element analyses have been carried out on cracked pipes and TPBB specimens to determine the stress triaxiality across the ligament. It is found that the stress triaxiality conditions across the ligament are similar for the specimen and the cracked pipes. Therefore, the specimen fracture parameters can be transferred to these cracked components. It is also verified from the experimental results that the specimen J–R curves also fall within the acceptable band of component J–R curves. These investigations emphasise the role of stress triaxiality in selecting the specimen type for transferring fracture parameters under large scale yielding.

Leak-before-break qualification of primary heat transport piping of 500 MWe Tarapur atomic power plant

Abstract The advent of Leak-Before-Break (LBB) concept has now replaced the traditional design basis event of the Double-Ended-Guillotine-Break (DEGB) to design the Primary Heat Transport (PHT) system piping of the Pressurised Heavy Water Reactor (PHWR) and Pressurised Water Reactor (PWR). This approach is being adopted to design the PHT system piping of 500xa0MWe Indian PHWR to be built at Tarapur (Tarapur Atomic Power Plant 3 and 4). The LBB concept basically demonstrates through fracture mechanics analysis that there is negligible chance of any catastrophic break of PHT pipes without prior indication of leakage. There are several steps in this work of LBB qualification, namely, evaluation of loads on the piping components, generation of tensile and fracture properties of PHT pipe base and weld material, determination of leakage size crack (LSC) and the elastic–plastic fracture mechanics (EPFM) and limit load analysis of the piping components with postulated LSC to evaluate the critical load at unstable ductile tearing and the limit load, respectively. The paper deals with the fracture analysis of the straight pipes and elbows of three pipe lines in the PHT system of TAPP 3 and 4. Three crack configurations are considered in the analysis. These are throughwall circumferential crack at the weld location of straight pipe and extrados of the elbow and throughwall axial crack at the elbow crown. In all the cases, necessary factor of safety with respect to the anticipated safe shutdown earthquake (SSE) load and LSC are shown to be more than the minimum required values for LBB qualification.

Derivation of ‘γ’ parameter from limit load expression of cracked component to evaluate J–R curve

Abstract Experimental evaluation of the J-integral requires the ‘ηpl’ function, proposed by Rice et al. [Progress in flaw growth and fracture toughness testing (1973) 231], to multiply the area under the load vs. plastic load-line-displacement curve. However, the J-integral, thus evaluated, requires modification if crack growth occurs. A ‘γ’ term was proposed by Hutchinson and Paris [Elastic–plastic fracture (1979) 37] and later generalised by Ernst et al. [Fracture mechanics (1979) 581] and Ernst and Paris [Techniques of analysis of load–displacement records by J-integral methods (1980)] to correct the J-integral to account for crack growth. The ηpl and γ functions are available for very few geometries under specific loading conditions. A limit load-based general expression of ηpl was given by Roos et al. [Int J Pres Ves Piping 23 (1986) 81], but no such expression is available for γ functions. The advantage of having limit load-based general expressions for ηpl and γ functions is that the limit load for a particular geometry subjected to a specific loading condition is easily available in the open literature. In the present paper, a limit load-based general expression for the γ function is derived. The general expression is then validated by deriving the known γ functions of various geometries subjected to various loading conditions, which are available in the open literature. The general expressions are then used to derive new ηpl and γ functions for same pipe and elbow geometries with various crack configurations under different loading conditions, for which no solutions are available in the open literature. Finally, experiments have been carried out on 200xa0mm nominal bore (NB) elbows with throughwall circumferential cracks under in-plane bending moment. The proposed new expressions of ηpl and γ functions for this geometry are used to obtain the J–R curve from the experimental load vs. load-line-displacement and load vs. crack growth data.

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.

Limit Load Equations for Miniature Single Edge Notched Tensile Specimens

While carrying out fatigue tests on miniature Single Edge Notched Tensile (SENT) specimens, one needs to know the limit load of the specimen to determine the maximum and minimum loads of fatigue cycle. In the literature, several limit load equations, for example, EPRI, Graba, Miller were available. There were large differences in the predicted values of these equations. Moreover, these equations were developed for conventional size of the SENT specimens. Although, limit load equations should be ideally size independent, it was not clear whether boundary effect of the miniature specimens is there or not. Therefore, it was important to investigate the accuracy of these equations and check whether they are applicable for miniature specimens or not. Consequently, detailed non-linear finite element analyses were carried out on a number of miniature SENT specimens to determine the limit load by twice elastic slope method. Elastic-perfectly plastic material behavior was assumed as is the convention. Based on these results, new limit load equations have been proposed for miniature SENT specimens. It was found that the present results match very closely with the prediction of Miller equation. However, they widely differ with respect to EPRI and Graba equations. Consequently, it is concluded that Miller equation is the most accurate to predict the limit load of SENT specimens and is applicable for miniature specimens as well without any boundary effect.

Determination of Fatigue Properties Using Miniaturized Specimens

It is very important to determine Paris’ power law constants to know the fatigue crack growth rate (FCGR) of a structure containing crack. These constants are generally determined by FCGR test using conventional specimens as specified by ASTM-E647 standard. This standard FCGR test procedure has placed strict size requirements on the conventional specimens and hence a large amount of material is needed to fabricate the specimens. However, sometimes, like in the case of testing of irradiated materials or nuclear pressure vessel surveillance, the material available for testing is not sufficient to make standard size specimens. Therefore, miniature specimens should be used to minimize the amount of material. In this work, constant load amplitude FCGR behavior of nuclear pressure vessel steel (20MnMoNi55) has been studied using miniature Single Edge Notched Tensile (SENT) specimens. The fatigue tests have been performed according to the procedure described in ASTM-E647 standard. The Paris’ power law coefficient and exponent obtained by FCGR test of miniature SENT specimens are in the range of 10−12 to 10−13 and 2.8–3.5 respectively, when the FCGR (da/dN) is expressed in m/cycle and stress intensity range (ΔK) in MPa√m. These values of Paris’ power law constants of miniature specimens are nearly of same order as that of the standard specimens where the results of standard specimens are taken from the literature.

Modelling of Irradiated Materials

Irradiation of materials by energetic particles causes significant degradation of the mechanical properties, most notably an increased yield stress and decrease ductility, thus limiting lifetime of materials used in nuclear reactors. The microstructure of irradiated materials evolves over a wide range of length and time scales, making radiation damage and inherently multi-scale phenomenon. At atomic length scale, the principal sources of radiation damage are the primary knock-on atoms that recoil under collision from energetic particles such as neutrons or ions. These knock-on atoms in turn produce vacancies and self-interstitial atoms, and stacking fault tetrahedra. At higher length scale, these defect clusters form loops around existing dislocations, leading to their decoration and immobilization, which ultimately leads to radiation hardening in most of the materials. All these defects finally effect the macroscopic mechanical and other properties. An attempt is made to understand these phenomena using molecular dynamics studies and discrete dislocation dynamics modelling.Copyright

Application of Modified Damage Potential (ψ-Integral) to Predict Crack Initiation in Welded Pipes and Experimental Verification

The mesh dependency of Rice and Tracey cavity growth factor (CGF) is overcome by integrating the CGF over a process zone surrounding the crack tip. This integral represents a modified damage potential. The critical value of the integral for crack initiation in weld material has been determined analyzing a welded CT specimen and comparing the computed crack initiation J with experimentally measured J-initiation value. This critical value is then employed to predict crack initiation load in 8” and 12” welded pipes having different measure of through-wall cracks at the center to predict the loads under four point bending loads. The computed values are compared with the experimentally measured values. A close agreement between the computed crack initiation loads with the experimentally measured values justifies the usefulness of the present modified damage potential.Copyright