How to extract more information from a basic tensile test ... plastic deformation ... border rolling...

FENet Annual Industry Meeting, Dec 3, 2004M. Juwet and D. Debruyne, KaHo St-LievenFENet Annual Industry Meeting, Dec 3, 2004M. Juwet and D. Debruyne, KaHo St-Lieven

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How to extract more informationfrom a basic tensile test with the

aid of FEA?

Marc Juwet and Dimitri DebruyneKaHo St.-Lieven - KULeuven

Belgium

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FENet Annual Industry Meeting, Dec 3, 2004M. Juwet and D. Debruyne, KaHo St-Lieven

“Basic” tensile test? •Initial geometry of specimen•Tensile force Fload (⇒ σload)•Elongation ∆L/L0 (⇒ e)

↓

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FENet Annual Industry Meeting, Dec 3, 2004M. Juwet and D. Debruyne, KaHo St-LievenFENet Annual Industry Meeting, Dec 3, 2004M. Juwet and D. Debruyne, KaHo St-Lieven

Associatie KULeuven

Uniform plastic deformation

σtrue = Fload/A = σload (1+e)εtrue = ln(A0/A) = ln(1+e)

Valid only before necking(ultimate tensile strength)

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A growing interest in complex FEA modelling

•Availability of powerful computers–CPU: speed (allows shorter computing times)–RAM: model size (allows higher accuracy)

•Better understanding of FEA in general

•Availability of sophisticated FEA software⇓

Increasing demand for complex FEA calculations(plastic deformation, contact modelling, crash simulations, etc.)

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Material is everything!!!

Every FE simulation starts with the input of material data(elastic and plastic behaviour for a mechanical problem)

↓For the metalforming industry the input of correct

material data is vital to the success of the FE simulation↓

From a basic tensile test one obtains the true plastic behaviour before necking

↓This is sufficient for many applications, but not all

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Plastic deformation beyond neckingExample 1: tubehydroforming

→

Necking can occur without fracturing of the tube

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Plastic deformation beyond neckingExample 2: border rolling

→

Circumference of initial hole is enlarged by 100%

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Plastic deformation beyond neckingExample 3: rupture disc (pressure relief)

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Deformation up to fracture at the nodes

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Goal of this investigation

We have (from basic tensile test)true plastic behaviour before necking

and engineering stress strain relation beyond necking↓

We need true plastic behaviour of material beyondnecking (ultimate tensile strength)

↑We can use

Analytical corrections: Bridgeman (not suited for thin plate)FE simulation of the tensile test (geometry independent)

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Research so far

Most theoretical studies deal with the question:“Given a certain material model (true stress true strain behaviour), how does necking occur and evolve up to fracture?”Material model ⇒ Theoretical stress strain diagramma

↔Very few studies deal with the far more interestingquestion:“Given an engineering stress strain diagramma, what is the true stress strain behaviour of the material?”Measured stress strain diagramma ⇒ Material model

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Basic Idea of a FE approach

Step 1: Propose a material model (based on reasonable assumptions)

↓Step 2: Simulate the tensile test and construct

the engineering stress strain curve↓

Step 3: Compare to experiment and correct the material model

(go back to step 2 until convergence is reached)

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Every day practice

•Given a certain geometry•Given certain material properties (i.e. conventional stress strain curve)•Given a certain failure mode

⇒ Redesign in a matter of days

⇒ We need a quick way to improve material data input

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Simple approach(fracture is not relevant)

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Tensile test on thin plate specimen

Krupkowski Power law: σ = C(ε0 + ε)n

→ C = 540 MPaε0 = 0,57%n = 0,237

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FE simulation of tensile test

More strain hardening is required beyond necking, butalready a good description up to strain values of 30%

→

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Propose a new material model

Plastic behaviour is adjusted beyond necking

Apply Voce equation:

σ = K (1 – m e-nε)

Taken into account thatσ|ε = ε(uts) = σ(uts)dσ/dε|ε = ε(uts) = σ(uts)

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Iterative FE simulation

Find optimum fit(e.g. least squares)

Satisfactory descriptionup to engineering strainvalues of 45%Local true strain in the necking zone is 85% !!!

This should be sufficient formost metalforming apps

Uniqueness?

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Extra check with different probe distances

Probe distance up tonow was 40 mm

What happens if thisdistance is altered?

⇓Extra information!

↓How to deal with this???

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Less simple approach(fracture is relevant)

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Incorporating fracture

•Many ways to do this– from very simple to very complex– physical and non-physical

•For FE simulation purposes we need– plastic behaviour of the material (stress vs. strain)– ánd damage accumulation (leading to fracture)

•Only relevant for high strain applications

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Example: Void material model(proposed by Gurson and extended by Tvergaard)

Based on physical grounds

Damage is accumulated by– Void growth– Void nucleation– Void coalescence

Critical void volume fraction

Loss of stress carrying capacity ⇒ Fracture21

Cu2O inclusionsin a Cu matrix

↓

⇓

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Void material model – new yield function

Stress state in a material separates into– hydrostatic part p (volume change)– deviatoric part s (plastic deformation)

These combine into the Von Mises stress q

New yield function– Material parameters q1, q2 and q3– Void volume fraction f

Hydrostatic stress contributes to plastic deformation for large voidvolumes (↔ Von Mises yield criterion)

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Void material model – void growth and nucleation

Change in void volume fraction fduring plastic deformation:

Due to growth:

Due to nucleation:

Material parameters fN, sN and εN(fN ≅ 0.04 sN ≅ 0.05 - 0.1 εN = 0.1 - 0.3)

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Stress vs. strainLess material has towithstand the sameamount of load Fload

Actual stress in the material grains becomesmuch higher as morevoids are formed

⇓

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Other stress strain behaviour is required

e.g. quadratic polynomials(by lack of a better alternative)

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Resulting engineering stress strain relations(after iterative FE simulations)

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ConclusionFE simulation of a basic tensile test can provideadditional information, but …

–from the experimental side: input is needed from more sophisticated tests for comparison purposes (e.g. determinationof void material parameters, true stress strain beyond necking)–from the theoretical side: as for material modelling beyondnecking and towards fracture, much is available, few is widelyapplicable–from the FEA view: uncertainties on element choices, implicit orexplicit scheme, uniqueness of the solution … (e.g. many authorsuse shell elements → incorrect!)

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Ongoing work: IUCE

Usage of optical camera measuringdevice in non-standard tensile tests(f.e. GOM, Limess)→ Strain fields (more information!)

Combined with iterative FE analysis(f.e. LCRS method) and refined experimental data processing→ Unique solution?

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Any questions?

[email protected]@kahosl.be

How to extract more information from a basic tensile test ... plastic deformation ... border rolling...

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