M. F. Kanninen

A FINITE ELEMENT CALCULATION OF STRESS INTENSITY FACTORS BY A MODIFIED CRACK CLOSURE INTEGRAL

Abstract An efficient technique for evaluating stress intensity factors is presented. The method, based on the crack closure integral, can be used with a constant strain finite element stress analysis and a coarse grid. The technique also permits evaluation of both Mode I and Mode II stress intensity factors from the results of a single analysis. Example computations are performed for a double cantilever beam test specimen, a finite width strip with a central crack, and a pin loaded circular hole with radial cracks. Close agreement between numerical results given by this approach and reference solutions were found in all cases.

A dynamic analysis of unstable crack propagation and arrest in the DCB test specimen

A simple analytical model is developed to accompany experimental work on rapid crack propagation and arrest in the DCB test specimen. The present work extends the beam-on-elastic foundation model used previously by taking account of shear deformation and of both translational and rotary inertia. Crack speeds predicted with the model are found to be in good agreement with the constant-speed behavior observed experimentally. It is demonstrated that kinetic energy makes an important contribution to maintaining unstable crack propagation and to crack arrest.

A critical survey on the application of plastic fracture mechanics to nuclear pressure vessels and piping

Plastic fracture mechanics techniques have been developed to treat the regime where extensive plastic deformation and stable crack growth occur prior to fracture instability in the tough ductile materials used in nuclear systems. As described in this paper, a large number of crack tip parameters can be used in a plastic fracture resistance curve approach. However, applications using the J-integral currently predominate. This parameter has significant advantages. It offers computational ease and can provide a lower bound estimate of the fracture condition. But, J also has a disadvantage in that only a limited amount of stable crack growth can be accommodated. The crack tip opening angle parameter, in contrast, can be valid for extensive stable crack growth. But, with it and most other realistic alternatives, the computational convenience associated with the J-integral is lost and finite element or other numerical methods must be employed. Other possibilities such as the two-criterion approach and the critical net section stress are also described in the paper. In addition, current research work focussed upon improving the theoretical basis for the subject is reviewed together with related areas such as dynamic plastic analyses for unstable crack propagation/arrest and creep crack growth at high temperatures. Finally, an application of plastic fracture mechanics to stress corrosion cracking of nuclear piping is made which indicates the possible anti-conservative nature of the current linear elastic assessments.

Preliminary Development of a Fundamental Analysis Model for Crack Growth in a Fiber Reinforced Composite Material

This paper describes the preliminary development of a mathematical model for the strength of fiber reinforced composites containing specific flaws. The approach is to embed a local heterogeneous region (LHR) surrounding the crack tip into an anisotropic elastic continuum. By direct consideration of the individual failure events that are activated near the flaw tip, a strength prediction can be made from the basic properties of the composites constituents. Computations for arbitrary flaw size and orientation have been performed for unidirectional composites with linear elastic-brittle constituent behavior. The mechanical properties were nominally those of graphite epoxy. With the rupture properties arbitrarily varied to test the capability of the model to reflect real fracture modes in fiber composites, it is shown in this paper that fiber breakage, matrix crazing, crack bridging, matrix-fiber debonding, and axial splitting all can occur during a period of (gradually) increasing load prior to catastrophic fracture. Qualitative comparisons with experimental results on edge-notched unidirectional graphite epoxy specimens have also been made.

Dynamic analysis of crack propagation and arrest in the double-cantilever-beam specimen

A simple one-dimensional analysis model was developed previously for rapid unstable crack propagation and arrest in wedge-loaded rectangular double-cantilever-beam (DCB) specimens. In this paper, the model is generalized to treat contoured specimens and machine-loading conditions. The development starts from the basic equations of the two-dimensional theory of elasticity with inertia forces included. Exploiting the beam-like geometry of the DCB specimen results in governing equations that are analogous to a variable-height Timoshenko beam partly supported by a generalized elastic foundation. These are solved by a finite-difference method. Crack propagation arrest results illustrating the effect of specimen geometry and loading conditions are described in the paper.

Crack arrest in steels

Abstract This paper examines 3 theories that have been used to characterize the arrest capabilities of steels and structures: (1) The static analysis, arrest toughness ( K Ia ) theory; (2) The dynamically loaded/stationary crack toughness ( K Id ) theory, and (3) The dynamic analysis, propagating crack energy or toughness ( R ID or K ID ) theory. These three concepts are examined in the light of measurements of unstable fracture and crack arrest in wedge-loaded DCB test pieces together with a fully dynamic analysis of the experiments.

A preliminary study of fast fracture and arrest in the DCB test specimen

This paper describes measurements of unstable fracture and arrest in a 4340 steel, wedge-loaded DCB (double cantilever beam) test specimen with a blunted starting notch but which is well below the limiting speeds predicted by Broberg and Yoffe, specimen which accounts for transverse inertia forces. Preliminary results of crack speed and arrest measurements are described and compared with results of the dynamic analysis. These results reveal that: (a) the inclusion of inertia forces in the equation of motion leads to substantial improvement in the prediction of crack speeds over previous quasi-static analyses, (b) a crack in a wedge-loaded DCB specimen tends to propagate at a constant velocity which depends upon the bluntness of the starting notch but which is well below the limiting speed predicted by Broberg and Yoffe, and (c) the kinetic energy in the system tends to be recovered. It is concluded that the wedge-loaded DCB test specimen shows promise as a vehicle for characterizing the dynamic fracture toughness and crack arrest capabilities of structural materials.

The Speed of Ductile-Crack Propagation and the Dynamics of Flow in Metals

In this paper the connection between the speed of ductile-crack propagation and the dynamic-flow properties of metals is examined. A theoretical analysis based on a dynamic solution for the Dugdale crack model and employing descriptions of 1) the strains within the plastic zone, 2) the rate dependence of the flow stress, and 3) a simple criterion for ductile fracture is developed. The calculations are found to compare favorably with observed crack speeds of 1.6 to 410 ft/sec in 0.00175-in.-thick steel foil. It is concluded that ductile-crack speed is limited by the increased resistance to plastic flow at high strain rates. The key factors determined in the analysis are used to show that flow stress data for strain rates exceeding 104 sec−1 can be extracted from ductile-crackpropagation experiments.

A Fatigue Crack Growth Analysis Method Based on a Simple Representation of Crack-Tip Plasticity

A new approach to fatigue crack propagation is described. The key element in the analysis is the inclined strip-yield superdislocation representation of crack-tip plasticity. The basis of the model is given and its potential application in a cycle-by-cycle analysis of fatigue crack growth under arbitrary cycle-by-cycle loads indicated. It is shown that, to perform a fatigue crack growth computation for a given load sequence, only the materials shear modulus, tensile yield strength, and Poissons ratio need to be specified. In the process, some account is taken of crack closure during the load cycle. Illustrative calculations for uniform cyclic loading are described and comparisons with experimental results made.

A Theoretical Model for Crack Propagation and Crack Arrest in Pressurized Pipelines

The further development of a mathematical model for steady-state crack propagation in a pressurized pipeline is described. A key parameter in the model-the location of the plastic yield hinge relative to the moving crack tip-was determined by forcing agreement with crack speeds observed in the full-scale line pipe tests. The maximum crack driving force predicted by the model was then taken as a measure of the minimum fracture toughness value required for crack arrest. Comparisons with existing empirical formulations derived by Battelle, the American Iron and Steel Institute, British Steel, and the British Gas Council for the minimum required toughness values for crack arrest were made to demonstrate the reasonableness of this approach.