Identification of mechanical properties from tensile and compression tests of unidirectional carbon composite Jan Krystek Tomáš Kroupa Radek Kottner

Outline Introduction Tensile test Two compression tests Identification of material properties Summary

Introduction Aim: Unidirectional composite material 5 independence component of stiffness matrix (C11 , C12 , C22 , C23 , C66) 5 independence material constant (EL, ET , GLT , υLT , υTT´) strength parameters (XT, XC, YT, YC, SL, α0) Stiffness matrix of transverse isotropic material Aim: Identification of mechanical properties using numerical simulation of tensile and compression test in FE system MCS. Marc and optimization algorithm in optiSlang software Material: carbon fibers Tenax HTS 5631 and epoxy resin

Tensile test Measured properties: EL, ET , νLT , XT, YT Tensile specimens Fracture of specimens

Fracture of specimen C-I_a → α0 = 57° Compression test - type I Measured properties: YC, α0 Fracture of specimen C-I_a → α0 = 57° Labelling Length Width Thickness YC [mm] [MPa] C-I_a 4.9 9.9 2.2 210 C-I_b 220 C-I_c 10.0 C-I_d 17.8 203 C-I_e 245* C-I_f 272* * incorrect fracture Compressive strength

Compression test - type II Measured properties: Labelling Length Gage length Width Thickness Fiber angle YC XC Failure [mm] [ °] [MPa] identification code C-II_a 165 5.0 25.0 1.1 90 185 - HAM C-II_b 170 10.0 2.2 175 AAT C-II_c 9.8 987 TAM C-II_d 853 XC, YC, α0 Fracture of specimens

Compression test specimen three-part identification codes Failure identification codes Compression test specimen three-part identification codes First character Failure mode Code Angled A Brooming B end-Crushing C Delamination D Euler buckling E tHrough-thickness H Kink bands K Lateral L Multi-mode M(x,y,z) long.-Splitting S Transverse shear T eXplosive X Other O Second character Failure area Code Inside grip/tab I At grip/tab A Gage G Multiple areas M Tab adhesive T Various V Unkwnow U Third character Failure location Code Bottom B Top T Left L Right R Middle M Various V Unkwnow U ASTM International: D 3410 Standard Test Method for Compressive Properties of Polymer Matrix Composite Materials with Unsupported Gage Section by Shear Loading. ASTM International, USA.

Comparison between linear and nonlinear models Identification of material parameters From experiment: In case of specimens with fibre angles between 15° and 75°, the nonlinear dependence of tensile force on displacement is obvious Nonlinear function with constant asymptote was used for shear modulus GLT in the process of identification: Comparison between linear and nonlinear models By means of otimization algorithms , the following function was minimized Parameters of optimization The strength criterion LaRC04 was used for identification of shear strength SL

Schema of identification process Identified material properties Identification of material parameters EL – elastic modulus in the longitudinal direction ET – elastic modulus in the transverse direction νLT – Poisson´s ratio GLT – shear modulus G0LT – initial shear modulus τ0LT – asymptote value of shear nLT – shape parameter XT – tensile strength in the longitudinal direction XC – compressive strength in the longitudinal direction YT – tensile strength in the transverse direction YC – compression strength in the transverse direction SL – shear strength α0 – angle of the fracture plane in pure transverse compression Schema of identification process Linear model Nonlinear model EL ET υLT GLT G0LT τ0LT nLT XT XC YT YC SL α0 [GPa] [ - ] [MPa] [ °] 120.0 8.0 0.337 4.0 4.6 115.0 1.2 1480 850 55 213 82 57 Identified material properties

Summary Specimens with different geometric properties were tested in tensile test and two types of compression tests The material parameters were identified with the use of numerical simulation of tests in finite element system MSC.Marc and optimization algorithms included in optiSlang software Failure criterion LaRC04 was used for the identification of strength parameters The nonlinear function with constant asymptote had to be used for description of material behavior up to fracture in the process identification In case of small displacement, the linear relationship can be used with sufficient accuracy