Micro-Scale Experiments and Models for Composite Materials

1. Micro-Scale Experiments and Models for Composite Materials • PhD-student:SanitaZike • Supervisors: • Lars P. Mikkelsen, DTU Wind Energy, • Section of Composites and Materials Mechanics • Bent F. Sørensen, DTU Wind Energy, • Section of Composites and Materials Mechanics • Viggo Tvergaard, DTU Mechanical Engineering, Section of Solid Mechanics PhDproject duration: 1. January 2012 - 31. December 2014 Project type & funding: PhD-A project, DCCSM Core (DSF)

2. Visionof PhD project The targetof the PhD project is to establish coupled modelling-experimental approaches for bridging the understanding of compositematerial properties from micro to macro scalelength.

3. Outline • Strain gauge measurements of soft materials • Plastic zone and shear band formation around notches • Single interface region study between fibre and matrix • Interaction between multiple fibre/matrix interfaces • Correlation between microscopic and macroscopic behaviour

4. 2. - 4. Plastic zone and shear band formation around notches & fibre/matrix interface References: Wang, G.F. & Van der Giessen, E., 2004. Fields and fracture of the interface between a glassy polymer and a rigid substrate. European Journal of Mechanics - A/Solids, 23(3), pp.395-409. Jeong, H.Y. et al., 1994. Slip lines in front of a round notch tip in a pressure-sensitive material. Mechanics of materials, 19(1), pp.29–38. Modelling and experimental determination of plasticity zone by formation of shear bands in polymer material around notches, single and multiple fibre/matrix interfaces.

5. Experimental testing Plasticity zone Glass – Polymer- Glass Cohesive laws References: Sørensen, B.F. et al., 1998. Fracture resistance measurement method for in situ observation of crack mechanisms. Journal of the American Ceramic Society, 81(3), pp.661–669. Sørensen, B.F. et al., 2010. Cohesivelawsforassessmentofmaterialsfailure: Theory, ezperimentalmethodsandapplication. DoctorofTechnicesthesis, DTU. .Goutianos, S., Frandsen, H.L. & Sørensen, B.F., 2010. Fracture properties of nickel-based anodes for solid oxide fuel cells. Journal of the European Ceramic Society, 30(15), pp.3173-3179. Interface studybetween glass and polymer introducing DCB testing method in optical microscope and ESEM

6. 5. Correlation between microscopic and macroscopic behaviour The ending of research project involves understanding the correlation between the observed micro- and macro-scale properties of composite materials. In micro-scale materials can sustain higher loads, therefore show better strength properties than the same materials in macro-scale. The project intention is to develop approaches, which can be used to predict macroscopic behaviour knowing the micro-scale properties.

7. 1. Strain gauge measurements of soft materials

8. Strain gauge as strain measuring device Resistivity change Strain Strain gauge electrical resistance is changed with small deformations of inner grids. Calibration of strain gauges has to be done to obtain gauge factor:

9. Aim and tasks • Aim: Obtain correction methods for strain gauge measurements • Tasks: • How measurement error varies with strain gauge type? • How much strain gauge measurements are influenced by specimen geometry and stiffness? • What is the impact of plastic deformation on strain gauge measurements? Purpose is to determine the measurements accuracy of strain gauges used in soft materials testing. Study involves: development of numerical model in FEM program ABAQUS; in situ micromechanical measurements under optical microscope incorporating digital image correlation (DIC) system

10. Recognition of problem Experimentally observed discrepancy between different strain measurement methods: Why SG, clip on and laser extensometer measurements show different strain values?

11. Strain distortions by ABAQUS

12. DIC measurements

13. Parameter study Variables: Elastic modulus of specimen Elastic and plastic deformation Strain gauge dimension Specimen dimension Pattern modification (elongation of end-loops) Length 1.5 - 10 mm Thickness 3.8 - 5.0 µm Thickness 1 – 30 mm Length 25 – 150 mm Width 10 – 25 mm

14. 2 D model MODELLING FEATURES: SG: uniform foil with ½ thickness (2D), elastic-plastic, back-to-back SGs Specimen: ¼ symmetry (3D), elastic, elastic-plastic Parts: solid, homogeneous, deformable Elements: plane stress & 3D stress Load: displacement boundary 3 D model

15. Gauge factor correction Manufacturers provided strain gauges are calibrated on stiff material - steel. Usage of strain gauges on softer material than constantan, requires new calibration or gauge factor correction. Gauge factor (GF) Gauge factor correction: Correction coefficient (C) – ratio between actual and SG determined strain:

16. Specimen thickness Strain gauge length & stiffness Parameter study results

17. Correlation between specimen thickness and strain gauge length thickness THICK THIN

18. Conclusions • Sufficiently large errors are observed even for relatively stiff specimens • Parametric study indicates major impact by gauge length and specimen thickness: • Shorter strain gauges are subjected to larger errors as strain distortions more affect measuring grid • Thinner specimens more affected by stiffening • Correction coefficient can be used to modify manufacturers provided gauge factor. Two correction coefficient values can be distinguished depending on specimen thickness. • At large strains, up to 5%: • Strain gauge reinforcement decreases due to plastic deformation of constantan. • Total reinforcement can either increase or decrease depending on specimen stiffness reduction during plastic deformation.