Facultad de Ingeniería 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 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 2
Introduction 3
Introduction Single Point Incremental Forming for skull implant Conventional Computer Numerical Control (CNC) milling machine 4
Why is so important to determine and to model the mechanical behavior of metals and alloys? Design and optimization of manufacturing processes of metals with permanent shape deformation e.g. sheet pile Estructural integrity of components FBO Engine test 5
How to determine the mechanical behavior of metals and alloys? Mechanical tests: Tensile tests Compression tests Biaxial tests Shear, plane strain Etc. 6
How to model the mechanical behavior of Ti64 alloy or other metals? Matematical formulations Phenomenological Physically based laws laws Based on micromechanics: Based on macroscopic Slip systems, nucleation, observations: load, viod growth, grain growth, stress, strain, etc. displacement fields 7
Modeling of mechanical behavior of materials by using Finite Element Method Simulations Material input Characterization from Finite data from of mathematical Element experiments models Software Young moduli Poisson coefficients Stress strain curves Lankfords (anisotropy) Initial yield points Strain fields (DIC) Etc. 8
Introduction State of the art: experimental observations Temperature dependent 9 Khan et al., 2004.
Introduction State of the art: experimental observations Strain rate dependent 10 Khan et al., 2004.
Introduction State of the art: experimental observations Anisotropic hardening 11 G. Gilles et al., 2011
Introduction State of the art: experimental observations Tension/compression asymmetry (yielding) Strength differential (SD) effect 12 G. Gilles et al., 2011
Introduction State of the art: experimental observations Plastic anisotropy Notched tensile specimen Initial Final cross-section cross-section 13
Introduction State of the art: constitutive modeling The macroscopic orthotropic yield criterion CPB06 * a a a F Σ k Σ Σ k Σ Σ k Σ 1 1 1 2 2 3 3 Notched tensile specimen k takes into account the strength differential effect (SD) a is the degree of homogeneity 1 , Σ C : S are the principal values of the tensor 2 , 3 C is a fourth–order orthotropic tensor that accounts for the plastic anisotropy C C C 0 0 0 S is the deviator of the Cauchy stress tensor 11 12 13 C C C 0 0 0 12 22 23 C C C 0 0 0 13 23 33 C 0 0 0 C 0 0 44 0 0 0 0 C 0 CPB06 Implemented in the Lagamine 55 0 0 0 0 0 C code by G. Gilles 66 14 * Cazacu et al., 2006
Introduction 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) 15
Outline 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 16
Experimental developments Implementation of tests at constant strain rate Machine vs specimen deformation durinf compression test SCHENCK Hydropuls 400 kN press
Experimental developments Implementation of tests at constant strain rate Tests at constant die speed (former method at MSM lab) X gl X gl Ramp X gl Displacement X gl Imposed displacement Time ( t=0 ) Time ( t=t 1 ) Time ( t=t 1 ) Time ( t=t n ) Time ( t=t n ) Time ( t ) = X ep Deformation of the specimen (Unknown) + X ma Deflection of the machine Time ( t=0 ) Time ( t=t n ) (Unknown) 18
Experimental developments Implementation of tests at constant strain rate Deflection of the machine (test without specimen) X ma X ma Ramp X ma Load Time ( t=0 ) Time ( t=t 1 ) Time ( t=t n ) Time ( t ) Time ( t=t 1 ) Load kN Displcement X ma - mm 19
Experimental developments Implementation of tests at constant strain rate Computation of the deformation of the specimen Measured - test 1 Measured - test machine Deformation of the specimen is computed X ep known 20
Experimental developments Implementation of tests at constant strain rate Strain vs time computation test at constant die speed + machine deflection forgotten H X t 0 ep t ln H 0 H initial height Strain rate is not constant 0 Strain evolution on the specimen is computed from X ep known 21
Experimental developments Implementation of tests at constant strain rate At the Time t * the machine deflection ( X * ma ) is known (for test at constant die speed) * X t , X X X ma gl ma gl 22
Experimental developments Implementation of tests at constant strain rate So we can compute the deformation of the specimen ( X ep ) (for test at constant die speed) X t X t X ( t ) ep Test1 gl Test1 ma 23
Experimental developments Implementation of tests at constant strain rate Also, theoretically we know ( X ep Theoretical ) for constant strain rate (for a test at constant strain rate) X ep t H exp t 1 0 24
Experimental developments Implementation of tests at constant strain rate Globlal displacement X gl Test 1 is computed (for the second test at constant strain rate) 25
Experimental developments Implementation of tests at constant strain rate Comparison constant and non-constant strain rate tests constant die speed(ramp ) V t constant (new method) Commonly used method is wrong 26
Outline 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 27
Experimental developments Implementation of tests at constant strain rate Comparison constant and non-constant strain rate tests 28
Experimental developments Implementation of tests at constant strain rate Important for strain hardening rate Compression 400°C Compression 600°C Strain hardening rate GPa constant constant non constant (ramp) non constant (ramp) y y p strain hardening rate y y 29
Outline 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 30
Validation of the method Digital Image Correlation setup Basic concept: DIC is measurement technique for full field non- contacting deformation and strain Step #2: calibration of Step #3: record Step #1: spray paint to the the cameras images of the event object (speckle pattern) Sample Calibration target Loading ( F ) Results: strain/displacement field Step #4: apply the correlation method 31
Validation of the method Digital Image Correlation setup 3D-DIC systems configuration SCHENCK Hydropuls 400 kN press Compression test 32
Validation of the method Strain field by DIC measurements Accurate displacement measurements and strain field computations reached Axial log. strain 33
Experimental results at RT Compression test for plastic anisotropy characterization barreling y coordinates - mm x coordinates - mm Strain distribution at dashed line Why axial zz strain is not homogeneous ? Friction effect? Plastic anisotropy? both ? 34
Why experimental axial zz strain is not homogeneous in compression tests? Numerical investigations of compression tests 1. Computation of Coulomb friction coefficient ST One-eight of the specimen is modeled Contact elements 1 st Inverse modeling of compression for computation of f 0.08 Iteration fitting Load + barreling VM identified with compression Verification with CPB06(4) barreling is more sensitive to friction than to anisotropy 35
Why experimental axial zz strain is not homogeneous in compression tests? LD Numerical investigations of compression tests horizontal centerline zz TD ST LD 36
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