IFMASS10

FRACTURE MECHANICS IN THE PLASTIC RANGE

Petar Agatonović

D-85244 Röhrmoos, Deutschland

1. INTRODUCTION

Fracture mechanics plays today a substantial role in the area of the investigation and

justification of structure integrity and in this respect it is very important instrument of the

engineering technology. With the help of fracture mechanics the relationships between

stress, crack size and material resistance to fracture can be calculated and evaluated for

different relationships. Here, a critical value of any one of the quantities can be

determined if the other two are known. For the purposes of the prediction and control,

fracture mechanics provides the adequate mathematical relationships between these

variables in the moment of failure. For example, if the design stress in the structure and

the fracture toughness of the material are specified, one can determine the critical flaw

size leading to the fracture. Compared to the traditional mode of integrity calculation that

relates applied stresses, for example, to the yield strength of the material, this is fully new

approach to the solution of the problem.

Within of the given structure the stresses are typically determined by the design, while

the fracture toughness is a property of the material. All materials contain flaws which

sizes and locations eventually can be determined by non-destructive testing method.

Resistance to fracture is the basic property of material contains the flaw. Main goal of

corresponding calculations in the design is the evaluation of the severity of the cracks,

existing in the structural elements, regarding the possible fracture and failure. Procedure

is based on principle that the failure appears when the applied load producing the growth

of the detected crack is larger than the material resistance to crack extension.

Key industries for economy any state depend very much on safe operation of plant

equipment and structures. General trend in the development and design methods is to

allow plastic loading with the aim not only to use properly modern materials of higher

strength, but also to extend the lifetime of the structure with the help of damage tolerance,

based on fracture mechanics methods. In this way, on the basis of integrity assurance the

large economic advantages can be achieved.

To this end, Linear Elastic Fracture Mechanics (LEFM) methods for the evaluation of

crack effect at load levels below and near yield strength, have been almost exclusively

used. They are adequate for some application but not effective and even dangerous in

many other situations, because they do not guarantee results on the safe side. But, a

sudden failure, as assumed in LEFM regime, is a rare event, although very spectacular

since it occurred by fast unstable crack propagation, in a most dangerous way, More

typical is the structural failure, accompanied by a plastic deformation and slow crack

extension, known as ’ductile failure’ or ’plastic collapse’. The plasticity effect in this case

can be explained considering energy nature of the fracture. Moreover, since in such a

case, a part of energy is spend for plastic deformation and the stress state is changed in