Plasticity 2

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Materials

Synopsis:

The course deals with an advanced applied plasticity - stress concentration in a plastic zone in front of a notch or a crack, limit theorems and their application in a the notch effect evaluation or in calculation of limit load of structural parts, response of an elastic-plastic body to the cyclic loading, plastic instability and a ductile fracture.

The emphasis is made especially on methods and results relevant to material sciences applications.

Requirements:

Plasticita 1 (14PLAS1)

Syllabus of lectures:

1. Stress concentration in the plastic zone around a ball-shaped cavity. 2. Stress concentration and fracture in the plastic zone in front of a notch - slip line method. 3. Principle of virtual work, lower-bound theorem, upper-bound theorem, energy dissipation in a surface of discontinuity. 4. Simple examples of limit analysis: tension of a bar with a hole, bending of a notched bar, punch indentation problem. 5. Limit analysis of engineering structures: bending of beams and frames, bending of plates, plastic hinge under a bending moment combined with an axial force or a tosion moment. 6. Cyclic plasticity: elastic and plastic shakedown, ratchetting and a connection with a high-cycle or low-cycle fatigue and plastic collapse. Cyclic stresses and plastic shear under the the contact. Rice's model of the cyclic stress state in the plastic zone in front of the fatigue crack. 7. Plastic tensile instability, necking and a ductile fracture of a bar and a thin strip. Bringman's stress, Gourson's model of a ductile fracture. 8. Bounds of elastic-plastic analysis and a transition to the brittle fracture. 8. Creep.

Syllabus of tutorials:

Study Objective:

Knowledge: Applied plasticity results which are important for material sciences: stress and strain concentration in plastic zones, analysis of a plastic load capacity using bound and upper theorems, cyclic plasticity - under contact of bodies and at a fatigue crack tip, plastic instability and the model of a ductile fracture.

Skills: Application of the konwledge mentioned above both in evaluation of the strength of present-day materials or structures and in development of new materials.

Study materials:

Key references:

[1] Tirosh, J. - Peles, S.: Bounds on the fatigue threshold in metals. Journal of the Mechanics and Physics of Solids 49 (2001) pp. 1301 - 1322.

Recommended references:

[1] Chen, W. F. - Han, D. J.: Plasticity for Structural Engineers. J. Ross Publishing, New York 2007.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: