PLASTICITY
Possible uses for this information will include:
· Providing useful information to self-learners;
· Providing focus for the developers of short courses, text books and other learning material;
· Providing a basis for the production of self-test quizzes and examinations;
· Providing the basis for registers of suitably qualified and experienced persons.
Recommended Competences
CategoryCode Number / STATEMENT OF COMPETENCE / Standard
or
Advanced
and
EQF Level / Resource
Reference
Code
Pre-Requisites
PLASpr1 / All learning outcomes in category FEA as appropriate to industry, application and level.
PLASpr2 / All learning outcomes in category MESM as appropriate to industry, application and level.
PLASpr3 / Appropriate learning outcomes in category CTD, MAS, NGEC and BMPS as appropriate to industry, application and level.
Knowledge
PLASkn1 / For a beam under pure bending sketch the developing stress distribution from first yield, to collapse. / S,6 / PLASref1
PLASkn2 / For a simple steel thick cylinder or sphere under internal pressure, state the location of first yield. / S,6 / PLASref2
PLASkn3 / State the ratio of Limit Load to First Yield Load for pure bending of a Beam and a Cylinder and Sphere under internal pressure. / A,7 / PLASref3
PLASkn4 / Sketch the variation of yield pressure and limit pressure for a cylinder with various ratios of radii. / A,7 / PLASref4
PLASkn5 / State the effect of including strain hardening effects on the collapse pressure of a component. / S,7 / PLASref5
PLASkn6 / List alternatives to the Twice Elastic Slope Criterion. / A,7 / PLASref6
PLASkn7 / Sketch a stress-strain curve for an elastic-perfectly plastic and bi-linear hardening material showing elastic and plastic modulii. / S,6 / PLASref7
PLASkn8 / Identify any restrictions on the use of material models with elements being used in any particular system. / S,7 / PLASref8
PLASkn9 / Identify the extent to which your application software allows modification of nonlinear material solution parameters. / A,7 / PLASref9
Comprehension
PLASco1 / Discuss salient features of the inelastic response of metals. / S,6 / PLASref10
PLASco2 / Explain the terms Isotropic Hardening, Kinematic Hardening and Rate Independency. / S,7 / PLASref11
PLASco3 / Discuss the role of the Hydrostatic and Deviatoric Stress Components in yield criteria for isotropic, polycrystalline solids. / A,7 / PLASref12
PLASco4 / Explain the terms Limit Load and Plastic Collapse Load and explain why the latter is often a misnomer. / S,7 / PLASref13
PLASco5 / Explain the terms First Yield Load, Ultimate Load and Plastic Instability Load. / S,7 / PLASref14
PLASco6 / Discuss the use of the Twice Elastic Slope Criterion and explain why this is sometimes used. / A,7 / PLASref15
PLASco7 / Explain the phenomenon of Shakedown and define the term Shakedown Load. / S,7 / PLASref16
PLASco8 / Contrast the terms Ratchetting and Low Cycle Fatigue. / S,7 / PLASref17
PLASco9 / Explain the Upper and Lower Bound Theorems. / A,7 / PLASref18
PLASco10 / Discuss the effects of stress singularities at re-entrant corners on limit load. / S,7 / PLASref19
PLASco11 / Explain how plastic effects in a Finite Element system are commonly handled as a series of incremental iterative linear analyses and contrast the Variable Stiffness, Initial Strain and Initial Stress approaches. / A,7 / PLASref20
PLASco12 / Explain, in general terms, the function of the Mises Flow Rule or Prandtl-Reuss Equations, used in a finite element solver. / S,7 / PLASref21
PLASco13 / Outline how the cumulative and incremental displacements, total strains, elastic strains, elastic stresses and plastic strains are related in the finite element solution algorithm. / A,7 / PLASref22
PLASco14 / Illustrate typical examples of Local Plastic Deformation and Gross Plastic Deformation. / S,7 / PLASref23
PLASco15 / Discuss the term Plastic Hinge. / S,6 / PLASref24
PLASco16 / Explain the significance of a Hysteresis Loop in a load/deflection test. / A,6 / PLASref25
PLASco17 / Explain the Elastic Compensation process. / A,7 / PLASref26
PLASco18 / Explain Melan’s Theorem and illustrate this via a deviatoric map. / A,7 / PLASref27
PLASco19 / Derive the load-displacement relationship for simple two or three-bar structures with elastic-perfectly plastic materials. Repeat the derivation for elastic strain hardening materials. / A,7 / PLASref28
PLASco20 / Discuss why implementation of the Tresca Criterion can cause numerical problems in an FEA solution and explain how you might get round the problem. / A,7 / PLASref29
PLASco21 / Explain the rationale behind the 5% strain limit in some codes of practice. / A,7 / PLASref30
PLASco22 / Describe the behaviour of common components in the plastic range. / A,7 / PLASref31
PLASco23 / Describe the Bauschinger Effect. / A,6 / PLASref32
PLASco24 / Describe the Limit Load Interaction Diagram for a rectangular beam under combined axial and bending loads. / A,7 / PLASref33
PLASco25 / Explain why finite element solutions tend to become unstable as the limit load is approached. / S,7 / PLASref35
PLASco26 / Discuss approaches employed to improve the finite element prediction of limit load. / A,7 / PLASref36
PLASco27 / Explain the process of Stress Redistribution. / S,6 / PLASref37
PLASco28 / Describe the process and common purpose of Autofrettage. / S,7 / PLASref38
PLASco29 / Describe, in general terms, how material models may be verified. / S,7 / PLASref39
PLASco30 / Describe how analysis drift from the desired constitutive behaviour may be monitored. / A,7 / PLASref40
PLASco31 / Discuss the general relationship between finite element mesh and size of plastic zone. / S,7 / PLASref41
PLASco32 / Describe the term Elastic Follow-Up. / A,7 / PLASref42
PLASco33 / Explain Neuber’s Rule. / A,7 / PLASref43
PLASco34 / Describe the Interaction/Bree Diagram for a rectangular beam under combined steady axial and cyclic bending loads. / A,7 / PLASref44
PLASco35 / Describe the generic Interaction/Bree Diagram for a structure under a combined steady mechanical load and cyclic mechanical load and the generic Interaction/Bree Diagram for a structure under a combined steady mechanical load and cyclic thermal load. / A,7 / PLASref45
PLASco36 / Derive the Interaction/Bree diagram for a two-bar structure with a steady tensile load and a cyclic thermal load applied to one of the bars. / A,7 / PLASref46
PLASco37 / Describe why the incompressible nature of plastic deformation can cause difficulties with analysis. / A,7 / PLASref47
PLASco38 / Explain the difference between Mohr-Coulomb and
Drucker-Prager yield surfaces. / A,6 / PLASref64
Application
PLASap1 / Define elastic perfectly plastic and bi-linear or multi-linear hardening constitutive data as appropriate. / S,7 / PLASref48
PLASap2 / Use FEA to determine Limit Loads for a range of components. / A,7 / PLASref49
PLASap3 / Use FEA to determine Plastic Collapse Loads for a range of components. / A,7 / PLASref50
PLASap4 / Use FEA to illustrate Shakedown for a range of components/structures and actions. / A,7 / PLASref51
PLASap5 / Use FEA to determine the presence of ratchetting for a range of components and actions. / A,7 / PLASref52
PLASap6 / Use tables and theoretical solutions as appropriate to evaluate first yield and limit loads for common components. / S,7 / PLASref53
PLASap7 / Using standard material data, derive a true stress
vs true strain curve to be used for nonlinear
analysis. / S,7 / PLASref65
Analysis
PLASan1 / Analyse the results from nonlinear material analyses of typical components and determine whether they satisfy design requirements. / A,7 / PLASref54
PLASan2 / Compare the results from nonlinear material analyses of components with allowable values and comment on findings. / S,7 / PLASref55
Synthesis
PLASsy1 / Specify the use of elastic perfectly plastic and bi-linear or multi-linear hardening constitutive data as appropriate. / A,7 / PLASref56
PLASsy2 / Plan a series of simple benchmarks in support of a more complex plasticity analysis. / A,7 / PLASref57
PLASsy3 / Plan modelling strategies for nonlinear material problems. / A,7 / PLASref58
PLASsy4 / Prepare an analysis specification for a nonlinear material analysis, including modelling strategy, highlighting any assumptions relating to geometry, loads, boundary conditions and material properties. / A,7 / PLASref59
PLASsy5 / Plan an analysis methodology for plastic
deformation under cyclic loading. / A,7 / PLASref63
Evaluation
PLASev1 / Select appropriate solution schemes for non-linear material problems. / A,7 / PLASref60
PLASev2 / Select appropriate idealisation(s) for components / structures, which are consistent with the objectives of the nonlinear material analyses. / A,7 / PLASref61
PLASev3 / Assess the significance of neglecting any feature or detail in any nonlinear material idealisation. / A,7 / PLASref62
PLASev4 / Assess the significance of simplifying geometry, material models, mass, loads or boundary conditions, on a non linear material analysis. / A,7 / PLASref34
REFERENCES:
PLASref1 Basic Engineering Plasticity, Rees DWA, Chapter 5.2, Elsevier Ltd, ISBN-10:0-7506-8025-3, 2006.
Pressure Vessels: Design and Practise, Chattopadhyay S, Appendix C1, CRC Press, ISBN 0-8493-1369-4, 2005
An introduction to modelling buckling and collapse, Falzon BG and Hitchings D, Chapter 6.3, pp. 80-82,
NAFEMS, ISBN-1 874 376 06 9, 2005.
PLASref2 Basic Engineering Plasticity, Rees DWA, Chapter 5.4, Elsevier Ltd, ISBN-10:0-7506-8025-3, 2006.
Mechanics of Materials, Benham PP et al, Chapter 14, pp389, Prentice Hall, ISBN-10:0582251648, 1996.
PLASref3 Basic Engineering Plasticity, Rees DWA, Chapter 5.3/5.4, Elsevier Ltd, ISBN-10:0-7506-8025-3, 2006.
Roark's Formulas for Stress and Strain, Young WC et al, Chapter 13, McGraw-Hill, ISBN-10:0071210598, 2002.
Theory of Plasticity, Chakrabarty J, Chapter 5, pp. 326/339, Butterworth-Heinemann, ISBN-10: 0750666382, 2006.
PLASref4 Pressure Equipment Technology, Banks WM (Ed.), pp. 69-70, John Wiley & Sons, ISBN-10: 1860584012, 2003.
Pressure Vessel Design: Concepts and Principles, Spence J (Ed.), Chapter 3, pp. 78-79, Spon Press,
ISBN-10: 0419190805, 1994.
PLASref5 Theory of Plasticity, Chakrabarty J, Chap 5, pp. 346-6, Butterworth-Heinemann, ISBN-10: 0750666382, 2006.
PLASref6 The Design by Analysis Manual, EUR-19030EN, Chapter 2.5.4, 2nd Revision and CD update,
published by the European Commission, 2001.
A Work criterion for Plastic Collapse, M Muscat et al, Int. J. Pressure Vessels & Piping, 80, pp. 49-58, 2003. A critical evaluation of plastic behaviour data and a united definition of plastic loads
for pressure vessel components, Gerdeen JC, Welding Research Council Bulletin, 1979;254.
PLASref7 Understanding Non-linear Finite Element Analysis Through Illustrative Benchmarks, Becker AA, Chapter 2, pp. 22, NAFEMS, ISBN-10: 1874376352, 2001.
PLASref8 System user manuals.
PLASref9 System user manuals.
PLASref10 An introduction to the use of material models in FE, Prinja NK and Puri AK, Chapter 4, pp.13-14,
NAFEMS, ISBN-1 874 376 06 9, 2005.
Understanding Non-linear Finite Element Analysis Through Illustrative Benchmarks, Becker AA, Chapter 2, pp. 17-20, NAFEMS, ISBN-10: 1874376352, 2001.
PLASref11 An introduction to the use of material models in FE, Prinja NK and Puri AK , Chapter 5.3, pp. 21-23,
NAFEMS, ISBN-1 874 376 06 9, 2005.
Understanding Non-linear Finite Element Analysis Through Illustrative Benchmarks, Becker AA, Chapter 2, pp. 27, NAFEMS, ISBN-10: 1874376352, 2001.
PLASref12 Understanding Non-linear Finite Element Analysis Through Illustrative Benchmarks, Becker AA, Chapter 2, pp. 24-25, NAFEMS, ISBN-10: 1874376352, 2001.
An introduction to modelling buckling and collapse, Falzon BG and Hitchings D, Chapter 6.5, pp. 84-85,
NAFEMS, ISBN-1 874 376 06 9, 2005.
Plasticity for Engineers, Calladine CR, Chapter 2.8, pp.32-37, John Wiley & Sons, ISBN 0-85312-884-7, 1985.
PLASref13 Pressure Vessel Design: Concepts and Principles, Spence J (Ed.), Chapter 3.3, pp. 75-78, Spon Press,
ISBN-10: 0419190805, 1994.
Pressure Vessel Design: The Direct Route, Zeman JL et al, Chapter 2, pp. 7-8 and pp.17, Elsevier Science,
ISBN-10: 0080449506, 2006.
PLASref14 Pressure Vessel Design: The Direct Route, Zeman JL et al, Chapter 2, pp. 6-10, Elsevier Science,
ISBN-10: 0080449506, 2006.
Understanding Non-linear Finite Element Analysis Through Illustrative Benchmarks, Becker AA, Chapter 4.2, pp. 109-110, NAFEMS, ISBN-10: 1874376352, 2001.
The Design by Analysis Manual, EUR-19030EN, Chapter 2.5.1, 2nd Revision and CD update,
published by the European Commission, 2001.
PLASref15 The Design by Analysis Manual, EUR-19030EN, Chapter 2.5.4, 2nd Revision and CD update,
published by the European Commission, 2001.
A Work criterion for Plastic Collapse, M Muscat et al, Int. J. Pressure Vessels & Piping, 80, pp. 49-58, 2003.
A critical evaluation of plastic behaviour data and a united definition of plastic loads
for pressure vessel components, Gerdeen JC, Welding Research Council Bulletin, 1979;254.
PLASref16 Pressure Equipment Technology, Banks WM (Ed.), pp. 67-71, John Wiley & Sons, ISBN-10: 1860584012, 2003.
Pressure Vessel Design: The Direct Route, Zeman JL et al, Chapter 2 pp. 8-9, Chapter 5, pp. 69-74, Elsevier Science, ISBN-10: 0080449506, 2006.
Pressure Vessel Design: Concepts and Principles, Spence J (Ed.), Chapter 3, pp. 81-84, Spon Press,
ISBN-10: 0419190805, 1994.
Pressure Vessels: Design and Practise, Chattopadhyay S, Chapter 2.1, CRC Press,
ISBN 0-8493-1369-4, 2005.
PLASref17 Pressure Equipment Technology, Banks WM (Ed.), pp. 67-71, John Wiley & Sons, ISBN-10: 1860584012, 2003.
Pressure Vessel Design: The Direct Route, Zeman JL et al, Chapter 2 pp. 8-9, Chapter 5, pp. 69-74, Elsevier Science, ISBN-10: 0080449506, 2006.
Pressure Vessel Design: Concepts and Principles, Spence J (Ed.), Chapter 3, pp. 81-84, Spon Press,
ISBN-10: 0419190805, 1994.
Pressure Vessels: Design and Practise, Chattopadhyay S, Chapter 2.1, CRC Press,
ISBN 0-8493-1369-4, 2005.
Pressure Vessels: Design and Practise, Chattopadhyay S, Chapter 3.4, CRC Press, ISBN 0-8493-1369-4, 2005
ISBN 0-8493-1369-4, 2005.
Understanding Non-linear Finite Element Analysis Through Illustrative Benchmarks, Becker AA, Chapter 2.8, pp. 57-60, NAFEMS, ISBN-10: 1874376352, 2001.
PLASref18 Plasticity for Engineers, Calladine CR, Chapter 4, pp.93-116, John Wiley & Sons, ISBN 0-85312-884-7, 1985
An introduction to modelling buckling and collapse, Falzon BG and Hitchings D, Chapter 6.4, pp. 82-83
NAFEMS, ISBN-1 874 376 06 9, 2005.
PLASref19 Pressure Vessel Design: The Direct Route, Zeman JL et al, Chapter 2, pp. 8 and 17 , Chapter 5, pp. 69-74, Elsevier Science, ISBN-10: 0080449506, 2006.
Pressure Vessels: Design and Practise, Chattopadhyay S, Chapter 4.3.3, CRC Press,
ISBN 0-8493-1369-4, 2005.
PLASref20 Understanding Non-linear Finite Element Analysis Through Illustrative Benchmarks, Becker AA, Chapter 2.3., pp. 29-30, NAFEMS, ISBN-10: 1874376352, 2001.