High strain rate characterization of unidirectional carbon-epoxy IM in transverse compression and in-plane shear via digital image correlation Pedro P. Camanho DEMec, University of Porto, Portugal Hannes Körber DEMec, University of Porto, Portugal Technische Universität München, Lehrstuhl für Carbon Composites, Germany José Xavier UTAD, Vila Real, Portugal

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions /19 1. Introduction Contents 1.Introduction. 2.Longitudinal compression tests. 3.Off-axis compression tests. 4.Analysis model. 5.Conclusions. 2

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions /19 3 Aircraft dynamic threats Crashworthiness. Bird strike. Tyre debris impact. Hard debris impact. Hail impact. Bird strikeHail damage [ Longitudinal Compressive ModulusLongitudinal Compressive Strength No consensus reached in previous studies; further investigations are required 1. Introduction

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions /19 4 Objectives To perform an experimental investigation of strain rate effects on the mechanical response of unidirectional carbon-epoxy composites: elastic, plastic and strength properties. uni-axial and multi-axial loading. To provide a sound scientific basis for the development of a strain rate dependent constitutive model. Materials and methods Hexcel IM CFRP used. Unidirectional test specimens. High-strain rate tests performed using a Split-Hopkinson Pressure Bar. The same specimen configurations and load introduction systems used in-quasi static tests performed in an universal test machine. 1. Introduction

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions /19 5 (Koerber and Camanho, Composites – Part A, in press, 2011). SHPB Experiment Simulation IM longitudinal compressive stress 2. Longitudinal compression [0] 12 UD laminate; nominal dimensions: 23x7x1.5mm 3

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions /19 6 Longitudinal stress-strain diagram Longitudinal modulus is not rate-dependent. Longitudinal compressive strength increases by 40% under dynamic loading. 2. Longitudinal compression

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions / Off-axis compression Experimental Setup Dynamic test setup Quasi-static test setup [θ] 32 UD laminate; θ=15˚, 30˚, 45˚, 60˚, 75˚, 90˚; nominal dimensions: 20x10x4mm 3 (Koerber and Camanho, Mechanics of Materials, Vol. 42, , 2010).

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions / Off-axis compression 15° off-axis compression (front view)30° off-axis compression (front view) 45° off-axis compression (side view)60° off-axis compression (side view) 75° off-axis compression (side view)90° transverse compression (side view) High strain rate failure modes In-plane shear dominated failure modes Transverse compression dominated failure modes

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions / Off-axis compression 15° off-axis compression30° off-axis compression45° off-axis compression 60° off-axis compression75° off-axis compression90° transverse compression

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions / ° Extrapolation of in-plane shear strength 30° 15° In-plane shear stress-strain response 3.Off-axis compression

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions / Off-axis compression Elastic domain, quasi-static. Elastic domain, dynamic. Failure domain, quasi-static. Failure domain, dynamic.

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions / Off-axis compression Transverse compressive modulus Shear modulus Transverse compressive strength In-plane shear strength

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions /19 4. Analysis model 13 Failure criterion:

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions /19 14 Two-parameter plasticity model 4. Analysis model Plastic potential (plane stress, no plastic deformation in the fiber direction): Associated flow: Equivalent stress: Effective plastic strain increment: (Sun and Chen, J. Composite Materials, Vol. 23, , 1989).

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions /19 15 Identification of model parameters 4. Analysis model selected so that all curves collapse into one master curve master

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions / Analysis model Model implemented in ABAQUS explicit as a material model using a VUMAT user subroutine. Forward-Euler integration scheme used for the stress update.

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions / Analysis model 15⁰ 30⁰ 45⁰60⁰ 75⁰ 90⁰

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions /19 18 The proposed modifications to the SHPB test methods enable a reliable measurement of the dynamic modulus and strengths of polymer composites. The longitudinal compressive modulus of elasticity in not strain rate sensitive up to the strain rates considered in this work. The longitudinal compressive strength increased 40% under dynamic loading. Under dynamic loading the transverse compression modulus of elasticty, yield strength and failure strength increased by 12%, 83% and 45% respectively. Under dynamic loading the in-plane shear modulus of elasticty, yield strength and failure strength increased by 25%, 88% and 42% respectively. The failure angle and friction coefficients used in the failure criteria are not affected by the strain rate. The experimental data obtained can be used to identify simple models that simulate the effect of strain rate on the plastic deformation and failure of composite materials. 5. Conclusions Conclusions

1. Introduction 2. Longitudinal compression 3. Off-axis compression 4. Analysis model 5. Conclusions /19 19 Tests at strain rates higher than 1000s -1. Investigate the effect of strain rate on the fracture toughness of composites. Enhancement of existing plastic-damage model by including strain rate effects. 5. Conclusions Future work