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Effect of small strain rate variations on the identification of the compressive behaviour of Ti6Al4V
Facultad de Ingeniería y Ciencias
14 eme Colloque National en calcul des structures 13-17 mai 2019, Giens (Var), France
Outline
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Effect of small strain rate variations on the identification of the - - PowerPoint PPT Presentation
Effect of small strain rate variations on the identification of the - - PowerPoint PPT Presentation
Facultad de Ingeniera y Ciencias Effect of small strain rate variations on the identification of the compressive behaviour of Ti6Al4V 14 eme Colloque National en calcul des structures 13-17 mai 2019, Giens (Var), France Outline
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SLIDE 3
3
Introduction
SLIDE 4
4
Conventional Computer Numerical Control (CNC) milling machine
Single Point Incremental Forming for skull implant
Introduction
SLIDE 5
Why is so important to determine and to model the mechanical behavior of metals and alloys?
5
Design and optimization of manufacturing
processes of metals with permanent shape deformation
e.g. sheet pile
Estructural integrity of components
FBO Engine test
SLIDE 6
How to determine the mechanical behavior of metals and alloys?
6
Mechanical tests:
Tensile tests Compression tests Biaxial tests Shear, plane strain Etc.
SLIDE 7
How to model the mechanical behavior
- f Ti64 alloy or other metals?
7
Matematical formulations
Phenomenological laws
Physically based laws
Based on micromechanics:
Slip systems, nucleation, viod growth, grain growth, etc.
Based on macroscopic
- bservations: load,
stress, strain, displacement fields
SLIDE 8
8
Modeling of mechanical behavior of materials by using Finite Element Method
Material input data from experiments
Young moduli Poisson coefficients Stress strain curves Lankfords (anisotropy) Initial yield points Strain fields (DIC) Etc.
Characterization
- f mathematical
models Simulations from Finite Element Software
SLIDE 9
Introduction
State of the art: experimental observations
Temperature dependent
9 Khan et al., 2004.
SLIDE 10
Introduction
State of the art: experimental observations
Strain rate dependent
10 Khan et al., 2004.
SLIDE 11
Introduction
State of the art: experimental observations
Anisotropic hardening
11
- G. Gilles et al., 2011
SLIDE 12
Introduction
State of the art: experimental observations
Tension/compression asymmetry (yielding)
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- G. Gilles et al., 2011
Strength differential (SD) effect
SLIDE 13
Introduction
State of the art: experimental observations
Plastic anisotropy
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Initial cross-section Final cross-section Notched tensile specimen
SLIDE 14
Introduction
State of the art: constitutive modeling
The macroscopic orthotropic yield criterion CPB06*
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Notched tensile specimen
* Cazacu et al., 2006
a a a
Σ k Σ Σ k Σ Σ k Σ F
3 3 2 2 1 1 1
CPB06 Implemented in the Lagamine code by G. Gilles
k takes into account the strength differential effect (SD) a is the degree of homogeneity
are the principal values of the tensor is a fourth–order orthotropic tensor that accounts for the plastic anisotropy is the deviator of the Cauchy stress tensor
3 , 2 1,
S C Σ : C S
66 55 44 33 23 13 23 22 12 13 12 11
C C C C C C C C C C C C C
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Identification of the constitutive model
- 1. Anisotropic elasto-plastic model
Yield criterion?
Orthotropic CPB06 characterized at several plastic work levels, temperatures and at 10-3 s-1
Hardening law?
Directional hardening: interpolation between the several yield surfaces of CPB06
Experimental tests required for the identification:
Tension LD (several temperatures), TD and ST directions Compression LD (several temperatures), TD and ST directions Plane strain LD direction (plane LD-ST) Shear strain ST direction (plane LD-ST)
Introduction
SLIDE 16
Outline
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Introduction Method for full range constant strain rate test Experimental results Validation of the method Effect of the strain rate variations on the
mechanical behavior of Ti6Al4V
Conclusions and perspectives
SLIDE 17
Experimental developments
Implementation of tests at constant strain rate
Machine vs specimen deformation durinf compression test
SCHENCK Hydropuls 400 kN press
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Experimental developments
Implementation of tests at constant strain rate
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Tests at constant die speed (former method at MSM lab)
Displacement Time (t) Ramp
Xgl
Imposed displacement
Xgl
Time (t=t1) Time (t=tn) Time (t=0) Time (t=0) Time (t=tn)
=
Deformation of the specimen (Unknown)
Xep Xma +
Deflection of the machine (Unknown) Xgl
Time (t=t1)
Xgl
Time (t=tn)
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Experimental developments
Implementation of tests at constant strain rate
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Deflection of the machine (test without specimen)
Load Time (t) Ramp
Xma
Time (t=t1) Time (t=0)
Xma
Time (t=t1)
Xma
Time (t=tn) Load kN Displcement Xma - mm
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Experimental developments
Implementation of tests at constant strain rate
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Computation of the deformation of the specimen
Deformation of the specimen is computed Xep known
Measured - test 1 Measured - test machine
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Experimental developments
Implementation of tests at constant strain rate
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Strain vs time computation
Strain rate is not constant Strain evolution on the specimen is computed from Xep known
height initial ln H H t X H t
ep
test at constant die speed + machine deflection forgotten
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Experimental developments
Implementation of tests at constant strain rate
At the Time t* the machine deflection (X*
ma) is known
gl ma gl ma
X X X t X ,
* 22
(for test at constant die speed)
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Experimental developments
Implementation of tests at constant strain rate
So we can compute the deformation of the specimen (Xep)
) (
Test1 Test1
t X t X t X
ma gl ep
23
(for test at constant die speed)
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Experimental developments
Implementation of tests at constant strain rate
Also, theoretically we know (Xep Theoretical) for constant strain rate
1 exp t H t X ep
(for a test at constant strain rate)
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Experimental developments
Implementation of tests at constant strain rate
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Globlal displacement Xgl Test 1 is computed
(for the second test at constant strain rate)
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Experimental developments
Implementation of tests at constant strain rate
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Comparison constant and non-constant strain rate tests
) speed(ramp die constant t V
method) (new constant
Commonly used method is wrong
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Outline
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Introduction Method for full range constant strain rate test Effect of the strain rate variations on the
mechanical behavior of Ti6Al4V
Validation of the method Conclusions and perspectives
SLIDE 28
Experimental developments
Implementation of tests at constant strain rate
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Comparison constant and non-constant strain rate tests
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Experimental developments
Implementation of tests at constant strain rate
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Important for strain hardening rate
strain hardening rate
p y y
(ramp) constant non constant
Compression 600°C
y
(ramp) constant non constant
Compression 400°C
Strain hardening rate GPa
y
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Outline
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Introduction Method for full range constant strain rate test Effect of the strain rate variations on the
mechanical behavior of Ti6Al4V
Validation of the method Conclusions and perspectives
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Basic concept: DIC is measurement technique for full field non-
contacting deformation and strain
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Validation of the method
Digital Image Correlation setup
Results: strain/displacement field
Calibration target
Step #2: calibration of the cameras
Loading (F)
Step #3: record images of the event Step #4: apply the correlation method Step #1: spray paint to the
- bject (speckle pattern)
Sample
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Compression test
SCHENCK Hydropuls 400 kN press
Validation of the method
Digital Image Correlation setup
3D-DIC systems configuration
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Accurate displacement measurements and strain field computations reached
Validation of the method
Strain field by DIC measurements
Axial log. strain 33
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Experimental results at RT
Compression test for plastic anisotropy characterization
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Why axial zz strain is not homogeneous ?
Friction effect? Plastic anisotropy? both ?
barreling
y coordinates - mm x coordinates - mm
Strain distribution at dashed line
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One-eight of the specimen is modeled
Contact elements
Why experimental axial zz strain is not homogeneous in compression tests?
Numerical investigations of compression tests
1. Computation of Coulomb friction coefficient
ST
1st Inverse modeling of compression for
computation of f 0.08
Iteration fitting Load + barreling VM identified with compression Verification with CPB06(4) 35
barreling is more sensitive to friction than to anisotropy
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Why experimental axial zz strain is not homogeneous in compression tests?
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zz
horizontal centerline
Numerical investigations of compression tests
TD ST LD LD
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Why experimental axial zz strain is not homogeneous in compression tests?
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Numerical investigations of compression tests
zz
Friction in compression tests influences the homogeneity
- f the axial strain field
Material Including friction Characteristic of strain distribution Isotropic Yes Inhomogeneous No Homogeneous Anisotropic Yes Inhomogeneous No Homogeneous
(Anisotropic) (Isotropic)
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Why experimental axial zz strain is not homogeneous in compression tests?
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Numerical investigations of compression tests with friction
(Anisotropic) (Strongly anisotropic sheet)
Friction enhances the visualization of the plastic anisotropy through the axial strain field in compression tests
Material Characteristic
- f
strain distribution Isotropic Weakly inhomogeneous Anisotropic Weakly inhomogeneous (different shape than isotropic) Strongly anisotropic sheet Strongly inhomogeneous
Compression sheet (stack)
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Two ways of computing the strain:
DIC or volume conservation (Eq. 1)
Validation of the method
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ln H t X H t
ep
- Eq. 1
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Two ways of computing the strain:
DIC or volume conservation (Eq. 1)
Validation of the method
40
Difference caused by barreling of the sample (friction)
SLIDE 41
Outline
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Introduction Method for full range constant strain rate test Effect of the strain rate variations on the
mechanical behavior of Ti6Al4V
Validation of the method Conclusions and perspectives
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Conclusions and perspectives
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Method for compression and tension tests at constant strain
rates using testing machine without PID control
Validation by two method, Volume conservation and DIC
measurements at RT by measuring the full strain field of the sample during testing
Effect of the strain rate variations on the mechanical behavior
- f Ti6Al4V
Mainly initial yield point Stress hardening rate
Axial strain sensitivity to the plastic anisotropy proposed for