Polymeric Foams Subjected to Direct Impact Loading Behrad Koohbor a - PowerPoint PPT Presentation

Dynamic Constitutive Response of Polymeric Foams Subjected to Direct Impact Loading Behrad Koohbor a , Addis Kidane a , Wei-Yang Lu b a . Department of Mechanical Engineering, University of South Carolina, Columbia, SC b . Sandia National Laboratories, Livermore, CA American Society for Composites 30 th Technical Conference Michigan State University, East Lansing, MI September 2015

Introduction and Motivation  Foams are engineering material of choice for applications requiring energy absorption and/or structural stability with reduced weight.  Often used in automotive and safety applications.  Many of their applications entail High Strain Rate loading conditions. Image courtesy of ERG Aerospace corporation

Introduction and Motivation  There are major challenges in the study of polymeric foams under dynamic loading conditions : 1) Low Impedance nature of the material 2) Change of Density during deformation

Challenge #1 Low Impedance nature of the material Which results in the Delayed stress/strain equilibrium Low transmitted signal Proposed Solutions:  Pulse Shaping o To increase the rise time and increase the stress uniformity in the specimen  Polymeric Bars or hollow tubes (applicable in SHPB) o To reduce the impedance mismatch between the specimen and the bars, in order to acquire transmitted signal  Thin Specimens o Shorten the wave reverberation time

Challenge #1 Low Impedance nature of the material Which results in the Delayed stress/strain equilibrium Low transmitted signal Proposed Solutions:  Pulse Shaping o To increase the rise time and increase the stress uniformity in the specimen  Polymeric Bars or hollow tubes (applicable in SHPB) o To reduce the impedance mismatch between the specimen and the bars, in order to acquire transmitted signal  Thin Specimens o Shorten the wave reverberation time

Challenge #1 Low Impedance nature of the material Which results in the Delayed stress/strain equilibrium Low transmitted signal Proposed Solutions:  Pulse Shaping  Polymeric Bars or hollow tubes (applicable in SHPB)  Thin Specimens o Shorten the wave reverberation time

Challenge #1 Low Impedance nature of the material Which results in the Delayed stress/strain equilibrium Low transmitted signal Proposed Solutions:  Pulse Shaping  Polymeric Bars or hollow tubes (applicable in SHPB)  Thin Specimens o Shorten the wave reverberation time Number of cells is not large enough to represent the material response at continuum scale

Challenge #1 Low Impedance nature of the material Which results in the Delayed stress/strain equilibrium Low transmitted signal Proposed Solutions:  Pulse Shaping  Polymeric Bars or hollow tubes (applicable in SHPB)  Thin Specimens Objective of this Work: Taking advantage of full-field measurements to calculate and include the effect of inertia stress into the analysis, as suggested in the literature *, ** . * Pierron F, Zhu H, Siviour C. 2014 Beyond Hopkinson’s bar. Phil. Trans. R. Soc. A 372 ** Othman R, Aloui S, Poitou A. 2010 Identification of non- homogeneous… Polym. Test . 29

Theoretical Approach  General Dynamic Stress Equilibrium:      b a (1) ij , j i i  Uniaxial Compression, Absence of Body Force Shear Stresses     z a (2)  z z  z   Acceleration = 0: cons . (3)  z      2  Acceleration ≠ 0: a dz (4) z z z z z z 2 1 1

Theoretical Approach L            L         L t t t a t d , 0 , , , z z z   0 Stress at position x=L and time t Stress measured at position x=0 and time t Inertia stress, which includes: Variation of ρ from z=0 to z=L • • Variation of a from z=0 to z=L

Challenge #2 Change of density during deformation (Compressibility) Proposed Solutions:  A one-dimensional model proposed to enable the calculation of local density, as a function of initial density ( ρ 0 ), local axial strain ( ε z ), and local plastic Poisson’s ratio ( ν ) Assumptions o Conservation of mass              1   d z t   ,     2 z , t    z , t exp z , t r z , t   z  0 d z , t z Local plastic Local density at Initial Local axial strain at Poisson’s ratio at position z and time t Density position z and time t position z and time t

Compressibility model           1       2 z , t z , t exp z , t 0 z Local density at Initial Local axial strain at position z and time t Density position z and time t

Direct Impact Experiments using Shock Tube  Piezotronic load-cells inserted behind the specimen (z = 0)  High strength aluminum projectile utilized  Different number of Mylar diaphragms (Strain rate applied on the specimen ( ε ): 2460 s -1 ) H 0 = 25.4 mm D 0 = 25.4 mm ρ 0 = 560 kg/m 3 (35 pcf)

Direct Impact Experiments using Shock Tube Stereovision high speed camera system used to capture the full-field deformation response:  Camera system -------------- Photron SA-X2 Cameras  Resolution --------------------- 384 × 264 pix 2  Frame rate -------------------- 100,000 fps ( 10 µs temporal resolution)  Stereo angle ------------------ 16.1 o stereo angle (Cameras mounted vertically)  Illumination system --------- High intensity LED white light  System triggered using oscilloscope  Load data and images acquired simultaneously using high speed DAQ

Direct Impact Results ρ 0 = 160 kg/m 3 ρ 0 = 640 kg/m 3 (10 pcf) (40 pcf)

Full-Field Density – Compressibility Model Local density of the material was calculated using the proposed model:              1   d z , t          2 z , t r z , t exp z , t z t ,   0 z  d z , t z Local density at Initial Local axial strain at position z and time t Density position z and time t    z , t r    z , t z    z , t

Full-Field Density – Compressibility Model Local density of the material was calculated using the proposed model:           1       2 z , t z , t exp z , t 0 z Local density at Initial Local axial strain at position z and time t Density position z and time t Up to ~6% increase in the density was calculated

Full-Field Acceleration Full-field acceleration a z (z,t) was calculated from the full-field displacement u z (z,t) based on a finite difference scheme:           1        a z , t u z , t t 2 u z , t u z , t t  z z z z 2 t

Evaluating the Inertia Term Numerical evaluation of the integral (inertia term):            z         z , t 0 , t , t a , t d z z z   0 n               z       i i i , t a , t d a s z   0  i 1 Number of slices used in this work (n): 25 Thickness of each slice ≈ 1 mm

Full-Field Stress and Strain            z         z , t 0 , t , t a , t d z z z   0

Full-Field Stress and Strain            z         z , t 0 , t , t a , t d z z z   0

Constitutive Response Local stress-strain curves obtained at different locations:

Constitutive Response Comparison with conventional measurement:

New Results – Higher Strain Rates H = 18 mm H = 28 mm D = 26 mm D = 26 mm Projectile Velocity = 123 m/s Projectile Velocity = 162 m/s

Summary  A non-parametric analysis was performed to include the concurrent influences of inertia stress and material compressibility into the dynamic deformation analysis of low impedance polymeric foams.  Full-field stress-strain response of the specimen was obtained using the non-parametric analysis.  The main limitation here was the time resolution of the system, which can be overcome using ultra high speed cameras currently available.  The method can be considered as a useful means to characterize low impedance and soft materials deformed at high strain rate conditions. Acknowledgements

New Results – Higher Strain Rates H = 28 mm H = 18 mm D = 26 mm D = 26 mm Projectile Velocity = 162 m/s Projectile Velocity = 123 m/s

Summary  A non-parametric analysis was performed to include the concurrent influences of inertia stress and material compressibility into the dynamic deformation analysis of low impedance polymeric foams.  Full-field stress-strain response of the specimen was obtained using the non-parametric analysis.  The main limitation here was the time resolution of the system, which can be overcome using ultra high speed cameras currently available.  The method can be considered as a useful means to characterize low impedance and soft materials deformed at high strain rate conditions. Acknowledgements