B. K. Dutta

Numerical investigations of crack-tip constraint parameters in two-dimensional geometries

Abstract In this study, detailed finite element analyses have been carried out on conventional laboratory specimens such as Centred Cracked Panel (CCP), Three Point Bend Bar (TPBB) and Compact Tension (CT) specimens to study the characteristics of crack-tip constraint parameters, Q and h . It is observed that the loss of constraint is gradual with increasing deformation for CCP, irrespective of crack depth and shallow cracked TPBB and CT geometries. Conversely, deeply cracked TPBB and CT geometries maintain high constraint to fairly high deformation levels. This paper also addresses the nature of crack-tip constraint conditions in axi-symmetric circumferentially flawed pipe (CFP). Two loading configurations are analysed: (a) CFP under axial pull only; and (b) CFP under internal pressure with associated crack-face pressure and axial pull. It is found that the axi-symmetric CFP under internal pressure exhibits lower constraint than those under pure axial pull. The radial compressive stresses resulting from internal pressure leads to stress biaxiality, which reduces the constraint.

A modified damage potential to predict crack initiation: theory and experimental verification

Abstract Mesh dependency of cavity growth model due to Rice and Tracey has been overcome by integrating it 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 SA333Gr.6 material has been determined analysing a CT specimen and comparing the computed J with the experimentally measured J -initiation value. The critical value of the integral was then used to compute J -initiation in other fracture specimens having different crack-tip constraints. The critical value was also used to predict crack initiation loads in three 8 in. straight pipes and three 8 in. elbows having different measure of through-wall circumferential flaws. The computed values have been compared with the experimentally measured values. A close agreement between the computed crack initiation loads with the experimentally measured values justified the usefulness of the present modified damage potential.

Analysis of crack-microcrack interactions and doubly kinked cracks using multiple singular points elements

The problems of crack-microcrack interactions and doubly kinked cracks have been analysed by the finite element method. In the first case the main crack tip SIF has been evaluated for different length of a collinear microcrack, which is located at a fixed distance. Through another case study the influence of a pair of stacked parallel microcracks on the SIF of a main crack has been studied by varying the spacing of the two microcracks. The third example deals with a doubly kinked crack. The SIF at the crack tip has been determined for various angles of the second kink. All the three examples have been studied employing the multiple point singularity elements and their degenerate forms. The finite element computations have been compared, whenever possible, with analytical solutions available in the literature. The accuracy of the finite element computations are good. This has been achieved using a relatively coarse discretisation.

A Mesh Independent GTN Damage Model and Its Application in Simulation of Ductile Fracture Behaviour

Ductile fracture process involves the typical stages of nucleation, growth and coalescence of voids in the micro-scale. In order to take the effects of these voids on the stress carrying capability of a mechanical continuum during simulation, damage mechanics models, such as those of Rousselier and Gurson-Tvergaard-Needleman (GTN) are widely used. These have been highly successful in simulating the fracture resistance behaviour of different specimens and components made of a wide spectrum of engineering steels. However, apart from the material parameters, a characteristic length parameter has to be used as a measure of the size of the discretisation in the zone of crack propagation. This inherent limitation of these local damage models prevents them from simulating the stress distribution near the sharp stress gradients satisfactorily, especially at transition temperature regime. There have been efforts in literature to overcome the effect of mesh-dependency by development of nonlocal and gradient damage models. A nonlocal measure (weighted average of a quantity over a characteristics volume) of damage is usually used in the material constitutive equation. In this paper, the authors have extended the GTN model to its nonlocal form using damage parameter ‘d’ as a degree of freedom in the finite element (FE) formulation. The evolution of the nonlocal damage is related to the actual void volume faction ‘f’ in ductile fracture using a diffusion type equation. The coupled mechanical equilibrium and damage diffusion equations have been discretised using FE method. In order to demonstrate the mesh independent nature of the new formulation, a standard fracture mechanics specimen (i.e., 1T compact tension) has been analysed using different mesh sizes near the crack tip and the results have been compared with those of experiment. The results of the nonlocal model have also been compared with those of the local model. The effect of different GTN parameters on the fracture resistance behaviour of this specimen has been studied for the nonlocal model and these results have been compared with those of experiment.Copyright

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.

A compatible and complete six-noded element to model singularity

Abstract The shape functions of a six-noded triangular element are developed to model power type singularities which satisfy all the convergence criteria—the rigid body mode, the interelement continuity and the constant strain condition. Hence this provides a unique tool to model power type singularities under mechanical and thermal loads. Three case studies are presented. The first case study deals with the comparison of the present element with the existing singular elements. The convergence studies are done for this case study by refining the mesh and also by increasing the order of integration. The second and the third case studies deal with real life problems, namely, the analysis of a cracked bimaterial strip and the analysis of a power plant nozzle with a kinked crack under mechanical and thermal loads. These case studies show the usefulness of the element.

Use of Two Singular Point Finite Elements in the Analysis of Kinked Cracks

ABSTRACT An element formulation is suggested to obtain variable order singularities simultaneously at two corner nodes of a side of a 4-noded quadrilateral. The element is useful for modelling a kinked crack with small kink length. The performance of the element is demonstrated by considering three different examples of kinked cracks. The path independency and the influence of mesh refinement on the computation of J integral are also examined.

Evaluating the Geometric Variation of Critical SZW in Mod9Cr1Mo Steel

In the present study, geometry-independent critical SZW has been experimentally and numerically determined in mod 9Cr1Mo steel. Relative crack size, thickness, standard and non-standard fracture specimen geometries have been considered. In the studied material, critical SZW has been found to be independent of relative crack size but dependent on thickness and fracture specimen geometry. As seen in the experimental results, minimum thickness criteria based on integral average stress measure provides better limiting thickness of fracture specimen.

Optimization of Process Parameters for Friction Welding of Bimetallic Welds

Bimetallic welds made between ferritic steels and austenitic stainless steels are conventionally fabricated using arc welding procedures such as Tungsten Inert Gas, Metal Inert Gas, Shielded Metal Arc Welding and Submerged Arc Welding. However friction welding provides a new and unique solid state approach for joining many similar and dissimilar materials, which may not be possible to join by other welding techniques available without adding any external filler metal. This approach is mostly used in joining of dissimilar materials. The reason for increased utility being the absence of any external filler material which may otherwise add to the heterogeneity of the weld structure. In this paper, the fabrication and effect of friction welding parameters on mechanical-micro structural changes of bimetallic weld joints has been discussed. An attempt has also been made to relate the effect of friction welding parameters on the peak temperature values taken near faying surface and micro hardness changes measured in various zones of weld.

The Effect of Throughwall Axial Crack on In-Plane Collapse Moment of Pipe Bend

A throughwall axial crack may develop in an elbow or pipe bend due to service related degradation mechanism. It is very important to know the plastic collapse moment (PCM) of an elbow in the presence of a throughwall axial crack. The existing PCM equations of throughwall axially cracked (TAC) elbows are either too conservative or inadequate to correctly quantify the weakening effect due to the presence of the crack. Further, they do not differentiate between closing and opening modes of bending although deformation characteristics under these two modes are completely different. Therefore, the present study has been undertaken to investigate through 3-D elastic-plastic finite element analysis. A total of 84 elbows with various sizes of axial cracks (a/Dm = 0–1), different wall thickness (R/t = 5 — 20), different elbow bend radii (Rb /R = 2,3) and two different bending modes, namely closing and opening have been considered in the analysis. Elastic-perfectly plastic stress-strain response of material has been assumed. Both geometric and material non-linearity are considered in the analysis. Crack closing is observed in most of the cases. To capture the crack closure effect, contact analysis has been performed. Plastic collapse moments have been evaluated from moment — end rotation curves by twice-elastic slope method. From these results, closed-form equations are proposed to evaluate plastic collapse moments of elbows under closing and opening mode of bending moment. The predictions of these proposed equations are compared with the test data available in the literature. Matching between predictions and experimental results is found to be satisfactory.Copyright