Mechanical Behaviour of silica filled Silicon Rubber: an Optical two-dimensional Extensometer Application Mechanics of Materials and Structures Lab (2MS) Engineering Materials Center (CMGD) Ales School of Mines (EMA) M. Giton, P. Ienny, R. Piques

CompTest Introduction Tear Strength: Common Approach n Principle: analytical model in Fracture Mechanics n Drawback: – no realistic approximation of the behaviour – dependency of the tear strength on specimen geometry loading conditions (type of the test) Local Approach n Principle: stress concentration analysis – Mechanical behavior of the material – Simulated test by FEA

CompTest Experiment Optimization processus Finite Element Analysis Load and Digital kinematic field constitutive law Boundary Conditions Mesh Optimization Procedure E xperimental D atas D igital I mage C orrelation I mage A nalysis E xperimental R esults FEA BC ED DIC IA ER M E(t) F(t)

CompTest Digital Image Correlation F(t) u(t) Experimental setup FEA BC ED DIC IA ER M Image sequence

CompTest Digital Image Correlation Principle of the method n two-dimensional displacement measurements FEA BC ED DIC IA ER M n Linear fit of displacement field n In-plane tensor of strain

CompTest Digital Image Correlation Image 2 X 1 Y 1 Y X X 2 Y 2 P 1 (x 1 ; y 1 ) M 1 M 2 P 2 (x 2 ; y 2 ) Image 1 Processing method FEA BC ED DIC IA ER M Elastomers: large strain Tear Study: local phenomena

CompTest Digital Image Correlation Image 2 X 1 Y 1 Y X X 2 Y 2 [F] P 1 (x 1 ; y 1 ) M 1 M 2 P 2 (x 2 ; y 2 ) Image 1 Improvement of the processing method FEA BC ED DIC IA ER M

CompTest Digital Image Correlation New correlation functions Iterative fine search method: lower number of intermediate images better localisation measurement u:Pattern of M FEA BC ED DIC IA ER M

CompTest Experimental Tests V UC UT BT B.C. Homogeneous tests FEA BC ED DIC IA ER M

CompTest Experimental Tests Exemple of experimental results in UT FEA BC ED DIC IA ER M

CompTest Experimental Tests Non-homogeneous tests LL RR a L geometry b  Alignment defaults FEA BC ED DIC IA ER M

CompTest Experimental Tests Non-homogeneous tests FEA BC ED DIC IA ER M Realistic mesh Realistic BC

CompTest Experimental Tests Non-homogeneous tests FEA BC ED DIC IA ER M Transverse profiles : axial stretch ratio evolution

CompTest Phenomenological model FEA BC ED DIC IA ER M

CompTest Experimental Study Numerical Study EXPERIMENTEXPERIMENT Testing  Images Collection Finite Element Analysis Load and Digital kinematic field viscous hyper- elastic law’s parametrers Boundary Conditions Mesh Optimization Procedure Finite Element Analysis Load and Digital kinematic field constitutive law Boundary Conditions Mesh E xperimental D atas D igital I mage C orrelation I mage A nalysis E xperimental R esults FEA BC ED DIC IA ER M

CompTest Finite Element Analysis constitutive law Boundary Conditions Mesh Optimization Procedure Law cost Function FEA BC ED DIC IA ER M

CompTest Results and Discussion Uniaxial Tensile Test

CompTest Results and Discussion Biaxial Tensile Test Pure shear

CompTest Results and Discussion DENT Test

CompTest Results and Discussion DENT Tests

CompTest Concluding and remarks Strain sollicitations diagram Multiaxial tests with localisation zone Fracture criteria

CompTest Concluding and remarks FEA + Two-dimensional Digital Extensometer Realistic Boundary Conditions Identical meshes for FEA/DIC Identification bases on Multiaxial Tests Inverse Approach