1. NAFEMS seminar, 31 May - 1 June 2006
ON THE MORE RELIABLE INTRODUCTION OF THE RESIDUAL STRESSES IN THE THERMO-MECHANICAL ANALYSIS OF LAYERED STRUCTURES
DUBRAVKA MIJUCA
Faculty of Mathematics
University of Belgrade
Serbia
ac.yu
NAFEMS seminar, 31 May - 1 June 2006
Prediction and Modelling of Failure Using FEA

2. Title
Note
Definition
This presentation is about use of the “new” finite element (FE) technology: The primal-mixed FE approach FEMIX HC, developed by the present author

3. Residual stresses are:
Note
Definition
Motive
Residual stresses are:
Stresses produced by non-uniform plastic deformations, thermal contractions or phase transformations. Often induced by the manufacturing process
Once the material has yielded during the loading process, residual stress and strains will remain even after external loading is completely removed
Cause no deformation until they are released by e.g. failure of the component

4. Definition
Motive
Failure
They cause damage in the form of cracks and delaminations in layered structures (composite)
The presence of residual stresses is another factor that adds to the uncertainties about structure performance

5. Motive
Failure
Goal
They act to enhance the potential for failure in engineering components.
For example: in components operating at high temperature, these stresses increase the likelihood for creep failure

6. Failure
Goal
References
To present the reliable primal-mixed FE approach where stresses, and thus residual stresses, are treated as solution variables, which enable its direct manipulation and introduction in analysis
Case studies that demonstrate use of the proposed FE approach in the analysis of layered structures will be presented (microelectronic packaging and wind turbines)

7. Goal
References
Koning HP, Fitzsimmons D (2005) A review of FEA technology issues confronting the aerospace industry. Paper proceedings NAFEMS World Conference, Malta
Schmauder S, Weber U, Soppa E (2003) Computational mechanics of heterogeneous materials––influence of residual stresses. Computational Materials Science 26: 142–153
Boczkowska A, Konopka K, Babski K, Krzesiński G, Kurzydłowski KJ (2005) Finite element modelling of the residual stresses in the ceramic–elastomer composites. Materials Science‑Poland, Vol. 23, No. 2:
Sørensen BF, Branner K, Stang H, Jensen HM, Lund E, Jacobsen TK, Halling KM (2005) Improved design of large wind turbine blades of fibre composites (Phase 2) - Summary Report Risø‑R‑1526
Kim JK, Lee DG, Cho DH (2001) Investigation of Adhesively Bonded Joints for Composite Propeller Shafts. Journal of composite materials, 35: 11
Duff IS (2002) MA57 – A new code for the solution of sparse symmetric definite and indefinite systems. RAL‑TR‑2002‑024
Brezzi F, Fortin M, Marini D (1993) Mixed finite element methods with continuous stresses. Mathematical Models and Meth. in Appl. Sciences. 3 (2):
Mijuca D (2004) On hexahedral finite element HC8/27 in elasticity. Computational Mechanics 33(6):466‑480
Mijuca D, Mastilović S (2005) A Novel One-To-One Multiscale Approach to Computational Mechanics of Materials, 1st International Workshop on Nanoscience & Nanotechnology IWON2005, November 15–18, pp. 180‑186

8. References Implication
Zarka J, Frelat J, Inglebert G, Kasmai-Navidi P. A new approach in inelastic analysis of structures, Martinus Nijhoff Publishers, Dordrecht (1988)
Hinton E. Introduction to Nonlinear Finite element analysis, NAFEMS Ltd (1992)
Liu W, Kriz RD (1999) Axial Shear Waves in Fiber-Reinforced Composites with Multiple Interfacial Layers Between Fiber Core and Matrix, Mechanics of Materials, 31:117‑129
Mijuca D, Ziberna A, Medjo B (2006) A Novel Primal-Mixed Finite Element Approach for Heat Transfer in Solids, Computational Mechanics, on‑line first
Bent F. Sørensen, Erik Jørgensen, Christian P. Debel, Find M. Jensen, Henrik M. Jensen, Torben K. Jacobsen and Kaj M.Halling (2004) Improved design of large wind turbine blade of fibre composites based on studies of scale effects (Phase 1) - Summary Report Risø-R-1390(EN)
Bucci RJ, Sklyut H, Mueller L, James MA, Ball DL, Donald JK (2005) Advances in Testing and Analytical Simulation Methodologies to Support Design and Structural Integrity Assessment of Large Monolithic Parts: A New Perspective, ASIP 2005,29 Nov – 1 Dec, Memphis, Tennessee
Akira Kuraishi, Stephen W. Tsai, and Julie Wan (2002) Material Characterization of Glass, Carbon,and Hybrid-Fiber SCRIMP Panels, SAND
Tan VBC, Deng M, Tay TE (2005) Coarse grained molecular modelling of composite interfaces. Materials Science Forum 502:39-44

9. Compressive vs. Tensile
References
Implication
Compressive vs. Tensile
They act as a driving force for localised creep strain accumulation.
If the stresses are highly triaxial only small amounts of creep strain is required before local failure
The potential for 3D residual stresses is greater in thick section components because there is greater material constraint preventing distortion.

10. Compressive vs. Tensile
Implication
Compressive vs. Tensile
FEA
Compressive residual stress has a beneficial effect on the fatigue life and stress corrosion because it delays crack initiation and propagation.
Tensile residual stress on the contrary reduces the mechanical performance of materials.

11. Compressive vs. Tensile
FEA
In MEMS devices
The presence of residual strains/stresses is often ignored in both CAE calculations and physical tests
Although they can have significant effects on performance of structure and contribute towards the lower component durability

12. In laminated composites
FEA
In MEMS devices
In laminated composites
As a result of the different thermal properties of each material/layer when subjected to the elevated fabrication process temperatures

13. In laminated composites
In MEMS devices
In laminated composites
Geometrical scales
They are usually developed in the layered structures by the thermomechanical mismatch between the compounds during cooling (or curing) from the fabrication temperature
The cause of warp in asymmetric layup.

14. In laminated composites
Geometrical scales
Vocabulary
Depending on the scale at which the matter is analyzed, different kinds of residual stresses are classically defined.
stresses of first kind: the macro stresses over a few grains,
stresses of second kind: over one particular grain
stresses of third kind: across sub-microscopic areas, say several atomic distances within a grain
The stresses of second and third kind are also called micro stresses.

15. Geometrical scales
Vocabulary
Stress
Prescribed stress – the stress will not change further.
Suppressed stress - the stress is zeroed
Unknown Stress State – it should be determined

16. Vocabulary Stress types Relation to strains
Prescribed stress override any other stress value at that node
Residual stress is a priori known stress which cause no deformation, but add its value to the calculated stresses due to the applied thermomechanical load.
Initial stress (pre stress) is stress from previous analysis (previous time step) which cause deformation, but vanishes if body is free to move. If boundary of the body is suppressed to move, it will add its value to the calculated stresses due to the applied thermomechanical load. Example: Initial stress in mechanical analysis due to the thermal deformation. Initial strain/stress option is mandatory for direst inelastic approach (Zarka [9])

17. Stress types
Relation to strains
Primal FE approach
Strain and Residual Stress

18. Where to enter by stresses directly?
Relation to strains
Primal FE
Primal-mixed FE
Where to enter by stresses directly?
Stresses are calculated a posteriori.
The residual stress field is impossible to introduce directly in the analysis.

19. Bridging with nanoscale
Primal FE approach
Primal-Mixed FE
Bridging with nanoscale
Allow more control over the design

20. Bridging with nanoscale Simple Example Initial stress
Primal-Mixed FE
Bridging with nanoscale
Simple Example Initial stress
Direct one-to-one coupling of FEMIX HC with atomistic molecular (MD) simulation (enables seamless semi‑coupling between length scales)
Molecular dynamics and embedded-atom interatomic potential is used on atomic scale.
Nanoidentation model problem
Edge dislocations on slip planes

21. Bridging with nanoscale Simple Example Initial stress
Initial stress (pre stress) txx=1, fixed boundary
Shear stresses not displayed: eq. to zero

22. Simple Example Initial stress
Residual stress
Initial stress (pre stress) txx=1, boundary free to move
All stress components are zeroed

23. Example Initial stress
Residual stress
Contour method
In the elastic range, the residual stress can just be added to the applied stress as a static load in primal approaches (introduce appr.error), and as a priori know stress in primal-mixed approaches.
When the total stress exceeds the actual yield strength, the material is plastically deformed.
Residual stress
Applied stress
Total stress

24. Residual stress Contour method Example
Destructive method for determination of the residual stress field.

25. Contour method
Example
CAD
Hypothetical example
The blade is of glass fibre/epoxy matrix pre-pregs
The gear box is made of fibre/epoxy
The adhesive is made of epoxy
External load - gravitational

26. Mijuca Dubravka, Finite element FEMIX HC EL
Example
CAD
Syy results
Mijuca Dubravka, Finite element FEMIX HC EL

27. Mijuca Dubravka, Finite element FEMIX HC EL
Syy results
+Residual stresses
Delamination
Mijuca Dubravka, Finite element FEMIX HC EL
Debonding
Crack

28. Mijuca Dubravka, Finite element FEMIX HC EL
Syy results
+Residual stresses
Rotor blade
Gravitational Load
Mijuca Dubravka, Finite element FEMIX HC EL
Gravitational Load and residual stress 1E6MPa

29. Mijuca Dubravka, Finite element FEMIX HC EL
+Residual stresses
Rotor blade
Pressure load from CFD
Mijuca Dubravka, Finite element FEMIX HC EL

30. Mijuca Dubravka, Finite element FEMIX HC EL
+Residual stresses
Rotor blade
Pressure load from CFD
Mijuca Dubravka, Finite element FEMIX HC EL
18789 dof’s per displacement vector and stress tensor
76.36 sec on the notebook 1.4GHz Intel Pentium (R) 512MB RAM

31. Mijuca Dubravka, Finite element FEMIX HC EL
Rotor blade
Pressure load from CFD
Conclusion
Pressure load on the upper side
Mijuca Dubravka, Finite element FEMIX HC EL

32. Reliable FEA consultancy and design
Pressure load from CFD
Conclusion
Thank you
The reliable fully three-dimensional reliable primal-mixed approach is recommended for the use in the analysis of layered structures where residual stresses should be taken in the account
Reliable FEA consultancy and design