ALBERT

Notes: Using the standard Rousselier ductile damage theory, a prediction is made of crack growth in the First Spinning Cylinder Test carried out by AEA Technology, Risley. Only data from small-scale mechanical tests and metallography have been used. The prediction has been “blind” in the sense that, although we were aware of the observed high J-R -curve (hitherto defying detailed interpretation by any of the standard fracture mechanics techniques), we restrained ourselves from any attempt to use the detailed results of the test itself in making the prediction. Indeed, we were in some confusion about the reported J-R-curves until a final meeting when our predictions were discussed with the experimental workers. Furthermore, crack growth versus rotation speed was predicted before sight of the experimental results.Originally, reasonable estimates of the size scale determining the averaging involved in the damage theory gave predictions of crack growth versus rotation speed which agreed very well with the cylinder test, except near initiation, where the apparent increase in initiation toughness was not predicted. These predictions involved the parameter J only through the use of the compact tension specimen results in fitting the damage theory parameters and were quite independent of any complications which might arise from the use of J when centrifugal or body forces are present. The J-R -curve predictions were not quite so good, but were still well above the small specimen results. Again, there was discrepancy near initiation.Subsequently, we have learned that metallography which we were led to believe applied to a section perpendicular to the line of the mean crack front in fact referred to a section parallel to the mean crack plane. A rough correction using limited additional data improves our “blind” prediction slightly, but other limitations of the available small-scale data mean that, had some suggestions in the literature been adopted, a result more in accord with that expected from the small-scale tests might well have been obtained. It is concluded that further development of the modelling and the associated large- and small-scale testing is required. Some comments on this further development and the potential of the method as a predictive engineering tool for the transfer of results from specimens to structures are made.

Notes: In this paper the Rousselier ductile damage model is used to simulate the softening behaviour of notched bars and crack growth in a pre-cracked specimen of an A508 pressure vessel steel. The effect of the internal parameters needed to represent the damage on the calculated results is studied. The interactions between these parameters and their effects on the calibration process are discussed. The effect of the cell size on the values of the damage parameters obtained during calibration and on the response of the specimens is briefly reviewed.

Notes: Abstract— The conventional use of continuum ductile damage mechanics in finite element analyses identifies the “cell” in which damage occurs with the finite elements in which the distribution of stress and strain is modelled. Since the cell size is a fixed, metallurgically-defined, property of the material being analysed, this methodology forces a minimum size for the finite element mesh. Mesh refinement is thereby disallowed. This paper presents one way of avoiding the problem by developing a mesh-independent cell model which, with a fixed cell size, allows the finite element mesh to be refined to any degree within the cells. Procedures which average some state variables within the cells are introduced to prevent the localisation of damage after a certain critical stage is reached. The method has been tested in numerical simulations of (a) the deformation of a notched tensile bar, (b) a 35 mm compact tension specimen and (c) the first of the AEA spinning cylinder tests. There is a reasonable agreement between the results of the computer simulations and those of the experiments.

Notes: Abstract— This paper reports on a three-dimensional numerical prediction that involves continuum damage theory for the deformation of centre cracked panels under uniaxial and biaxial tensile loading. The predicted differences of crack tip blunting movement, crack tunnelling behaviour and the changing shape of the plane ahead of the crack tip for the two loadings are close to those observed in tests. The material parameters that encapsulate the damage response of the A533 B class 1 steel tested, were selected from a detailed parametric study on laboratory crack-growth resistance tests on the material.

Notes: Abstract— Under a natural mapping between the standard R-curve analysis diagram and the failure assessment diagrams of R6 and PD6493 Level 3 the R-curve becomes the RCI (R-curve image). It follows that whenever the assessment point moves along the failure assessment line during ductile crack growth, the implication is that the failure assessment line is the RCI. This result is used to test the conservatism of a specific PD6493 Level 3 analysis by two methods. The first calculates the variation during crack growth of the applied elastic-plastic crack tip opening displacement (CTOD) parameter (or‘driving force') which is implied by the PD6493 analysis and then compares this variation with an independent estimate of it. The second uses an assumed driving force to deduce the CTOD resistance curve implied by the failure assessment line. It is shown by both methods and also by a direct R-curve analysis that this particular PD6493 analysis is conservative relative to an R-curve analysis which uses a crack driving force estimated by the EPRI (Electric Power Research Institute) procedures. However there is inconsistency between standard R-curve analysis and PD6493 Level 3 analysis in that the latter implies a material resistance which, for a given material, depends on the geometry of the structure. A similar inconsistency arises in any failure assessment procedures like the Options 1 and 2 with Category 3 of R6, which require the assessment point to move on a geometry independent failure assessment line during crack growth; indeed, even when the failure assessment line is geometry dependent there is full agreement with R-curve analysis only if the correct RCI is used as the failure assessment line. In a brief discussion it is noted that the new failure assessment diagram studies involving multi-parameter fracture mechanics may help to ameliorate these problems.

Notes: Abstract It is emphasized that the science and crafts associated with the parting of solids are of considerable industrial, cultural and historical interest. Some principles of the modern theory of fracture which may be relevant to the controlled separation of a solid into pieces are reviewed. The use of path independent integrals in the analysis of indentation fracture is discussed, and some of the subtleties involved in treating the motion, deviation and forking of cracks and the energy balance in crushing and shattering are considered. The paper concludes with a brief account of some recent work on the theory of flint knapping and of the influence of the environment on the fracture process.