Course content

Theory of plasticity; fundamental equations. Applications to metal forming (Slab method, bound-teqniques, plane strain slip line solutions)
Constitutive equations for hot forming (Zener-Hollomon equations, determine parameters, testing methods, sensitivity-analysis)
Formabilty of thin-walled sheets and sections (Strain-hardening, anisotropy, crystal plasticity, strain localisation, damage evolution, shear fracture, forming limit diagram FLD, importance of the shape of the flow surface at the loading point)
Extrusion of aluminium sections; theory and praxis
Stretch-bending and local forming; theory and praxis (hydroforming, intending and incremental forming) of thin-walled aluminium sections and sheets
Finite Element Method (FEM). Flow analysis, friction modelling, tools and dies; loads,variability, optimalisation.
Innovations in the value chain from billet to final component or system.

Learning outcome

Knowledge: The course shall give the candidate knowledge on: Basic theory of elasticity and plasticity; equilibrium; compatibility; constitutive equations/models; forming mechanisms and influential parameters; analysis methods; friction and friction models; thermal effects; accuracy and dimensional capability of end product; industrial factors that affect the interplay between product and forming process; knowledge based choice of suitable solutions and parameters; forming related problems within the scope of PhD subject of candidate.
Skills: The candidate shall master the following: Apply basic plasticity theory for establishing analytical/numerical solutions for forming problems within extrusion, forging and/or forming of thin-walled profiles and sheets; understand the practical aspects of the interplay between tools, elastic-plastic deformation and product properties (quality) for different aluminum forming processes; skills for establishing representative models (FEA, analytical) for forming processes: perform simplified calculations for more effective and correct evaluation of critical aspects related to metal forming; provide the basic capabilities for evaluation of validity of results obtained by numerical methods (FEA), along with understanding the effect of various parameters.
General competence: The candidate shall on general basis: Be capable of collecting information and research results from various sources; establish a strategy for own research based on needs and gaps; identify and systematically solve research related problems; communicate and disseminate results from own and others research through reports and other media; view her/his own research in a wider perspective than the academic one.

Learning methods and activities

Half the course is given as lectures and exercises. 4 of 5 exercises have to be accepted before final exam(Exam 50% wieght of final score)
The other half of the course is an individual semesterproject. The student selects a topic of his interest in the field of metall plasticity and forming processes related to aluminium extrusion and its downstream processes. The project is worked on through the whole semester. A repport is submitted 2 days before final presentation. The weight of the score is 50% of total score. To pass the course a score of at least 70 percent is required.

Compulsory assignments

• Exercises and semesterproject

Recommended previous knowledge

Strength of Materials
Continuum mechanics
Materials and prosesses, introduction

The course will only be given if there is a sufficient amount of students (at minimum 2) that have the course as a part of their obligatory course work.

Course materials

Wagoner, R.H. & Chenot, J.-L.: "Metal Forming Analysis" Cambridge University Press 2001

Theory and Practice of Aluminium Extrusion
- Støren, S. & Mo, P.T.: "Extrusion" Ch. 8 in Handbook of Aluminium Vol. 1. Physical Metallurgy and Processes (Eds.:Totten, G.E. & MacKenzie, D.S.), Marcal Dekker 2003, pp. 385- 480
- Støren, S.: Lecture Notes

Sheet Metal Formabilty
- Marciniak, Z. & Duncan, J.: "Mechanics of Sheet Metal Forming" Ch. 3.: "Tensile instability". Edward Arnold 1992
- Støren, S. & Rice, J.R.: "Localized necking in thin sheets" Journal of the Mechanics and Physics of Solids 23 (1975) 421-441

Stretch bending and Local Forming of Aluminium Section
- Welo, T.: "Bending and Forming of Aluminium Sections" Compendium

Selected articles
- Kuroda, M. & Tvergaard, V.: "A phenomenological plasticity modell with non-normality effects representing observations in crystal plasticity". Journal of the Mechanics and Physics of Solids 49 (2001) 1239-1263
- Hwang, Y.-M. & Lin, Y.-K.: "Analysis and finite element simulation of the tube bulge hydroforming process". Journal of Materials processing technology 125-126 (2002) 821-825.

Credit reductions