HIGH VELOCITY IMPACT UNDER AXIAL CRUSHING AND BENDING COLLAPSE ON THIN-WALLED PRISMATIC STRUCTURES THESIS Submitted in partial fulfillment of the requirements for the degree of Master of Engineering from the Institut Teknologi Bandung by TRAN HAI NIM : 23613011 Aeronautics and Astronautics Study Program Faculty of Mechanical and Aerospace Engineering INSTITUT TEKNOLOGI BANDUNG 2015 HIGH VELOCITY IMPACT UNDER AXIAL CRUSHING AND BENDING COLLAPSE ON THIN-WALLED PRISMATIC STRUCTURES By TRAN HAI NIM : 23613011 Aeronautics and Astronautics Study Program Faculty of Mechanical and Aerospace Engineering Institut Teknologi Bandung Approval of Supervisory Committee Date: 16, Feb 2015 Advisor Dr. Leonardo Gunawan NIP.196211111989101001 Co–Advisor Dr. Sigit Santosa Dr. Tatacipta Dirgantara NIP.19700424 200604 1018 ABSTRACT Master’s Thesis HIGH VELOCITY IMPACT UNDER AXIAL CRUSHING AND BENDING COLLAPSE ON THIN-WALLED PRISMATIC STRUCTURES By TRAN HAI NIM: 23613011 Thin-walled prismatic structures are one of the most efficient energy absorbing components in various engineering systems such as components of automobiles, aircrafts, ships and trains.
They are widely used in buses, coaches, special purpose vehicles, and other areas subject to safety requirement. Especially, in modern society, transportation vehicles have higher speed and lager size. Therefore, thin-walled structures become more important to absorb impact energy and prevent high deceleration on the passengers during high velocity impact. This research investigates the behaviors as well as assesses the effect of strain rate to energy absorption capability of prismatic thin-walled structures subjected to high velocity impact under axial crush loading.
In addition, this research will also study the bending collapse behavior of thin-walled beams. In particular, the deep plastic collapses of the thin-walled beams so that one can predict the ultimate strength and energy absorption capability. For high velocity impact under axial crush loading, the dynamic behavior of thin-walled square columns is examined by analytical and numerical analysis. An explicit-nonlinear commercial finite element code LS-DYNA is used to predict the response of thin-walled square columns subjected to high velocity under axial crushing conditions.
It revealed the effect of the impact velocity i and strain rate of material during dynamic plastic buckling progression. The strain rate sensitive material- mild steel St-37 is utilized in this study since its stress-strain relation depends on the strain rates. Two groups of material models are used, one group has strain rates up to 100 s-1 and the other group has strain rates up to 4500 s-1. The study is conducted by using analytical solution and finite element analysis for impact speeds of 10 m/s, 20 m/s, 30 m/s, 40 m/s and 50 m/s.
Results indicate that for the impact speed less than 20 m/s, there are no significant differences on the crushing forces. However, for impact speed higher than 20 m/s, the crushing forces of the columns with material model covering strain rates up to 4500 s-1 are higher than those obtained using material model covering strain rates up to 100 s-1. The results suggest that analysis of high velocity impact should be performed with material model covering high strain rates. Furthermore, the compared results between analytical and numerical analysis have a good agreement in term of mean crushing forces and energy absorption capability of thin-walled structures under high velocity impact loading.
The axial impact under high velocity conditions for strain rate sensitive material, the peak crushing force, the energy absorption capability and mean crushing force are higher than that of lower velocity. The bending response of thin-walled beams is studied through numerical and experimental studies in quasi-static and dynamic cases. A combination of analytical and numerical results is used to predict the initial and post collapse response of the thin-walled beams. The experimental validation was used to confirm analytical and numerical prediction of bending crush behavior of the thin-walled beams, such as peak moment, moment-rotation and energy absorption.
ii Acknowledgements First and foremost, I would like to express my deepest gratitude to my advisors, Professor Ichsan Setya Putra, Dr. Leonardo Gunawan, Dr. Sigit Santosa, Dr.Ir Tatacipta Dirgantara and Dr. Ly Hung Anh, for their dedicated guidance and conscientious helping of this research.
I also indebted a grateful thank to Dr. Annisa Jusuf, Dr. Hery Setiawan who have support me in many and various ways during this study. My appreciation goes out to Technical staff Mr.
Eddi Satriyo Wibowo and Engineer from General Motor, Indonesia Mr. Didi Nuryadi Arifin who did not hesitate in helping to procure the specimens for the experiments. I greatly appreciate helping from Metal Industry Development Center (MIDC), Bandung, Indonesia where many experiments in my research were executed. I gratefully acknowledge AUN/SEED-Net, JICA for the financial support.
All of that supports help me to have a peace of mind and spent the entire time to complete this study in the best way. Thank are due to many my friends, my colleagues at Lightweight Structure Laboratory, Institut Teknologi Bandung, who have always been willing to offer advices. Many grateful thanks to my best friend Mr. Vu Tien Dat who always shares and helps me in my research.
This last group of people has the greatest influence on my life. My father Tran Thanh and my mother Nguyen Thi Mung have support me emotionally throughout my academic career. To them I love with all of my life. I also would like to express my deep gratitude to my sisters Tran Thi Huong, Tran Thi Anh Nga and Tran Thi Hien, and my brothers Tran Hoa, Tran Khoa, who were always supportive Finally, I want to thank my girl friend Ms.
Nguyen Kim Ngoc Hien, who has been waiting and always supported me in any circumstances. Within her love, her patience, I have worked and tried to finish well the master program in ITB. iii Contents Abstract. iii Table of Contents.
iv List of Figures. vii List of Tables. xii List of Symbols. xiii Chapter 1: Introduction.2 Research objectives and methodology.
8 Chapter 2: Literature Review and Theoretical Background .2 Axial crushing collapse .2 Strain rate sensitive material .3 Bending collapse on thin-walled prismatic beams .1 Theoretical bending collapse mechanism of prismatic thin-walled beams .2 Effect of strain rate in bending collapse.4 Idealized material model .1 Small plastic deformation .2 Large plastic deformation .5 Crashworthiness parameters in axial crushing .1 Initial peak force .2 Mean crushing force .4 Energy absorbed per unit length .5 Crushing force efficiency .6 Theoretical prediction of static and dynamic progressive buckling in axial crushing of thin-walled square columns .1 Static axial crushing of thin-walled square columns .2 Dynamic axial crushing of thin-walled square columns. 39 Chapter 3: Axial Crushing of Thin-Walled Prismatic Columns under High Velocity Impact .1 Finite element analysis of thin-walled square columns under axial impact .1 Explicit finite element solver .2 Dynamic simulation of thin-walled square columns under axial impact .2 Finite element modeling .1 Effect of element size .2 Effect of initial impact velocity .3 Effect of thickness of thin-walled columns.4 Effect of trigger mechanism .5 Effect of strain rates. 59 Chapter 4: Bending Crush Behavior of Prismatic Thin-Walled Beams .1 Bending crush resistance of prismatic thin-walled beams .2 Finite element modeling .4 Experiment set up .5 Numerical and experimental results .1 Effect of frictionless coefficient .2 Effect of geometrical imperfection .3 Effect of thickness of thin-walled beams .6 Dynamic bending response of thin-walled beams .1 Effect of strain rates .1 Numerical simulation model and experimental set up .2 Numerical and experimental results. 94 Chapter 5: Summary, Conclusions and Future Works .1 Summary and conclusions.
Three point bending quasi-static test certificate from MIDC. Drawings of apparatus of three point bending dynamic drop test. 110 vi List of Figures 1.1 Distribution of type of collision of passenger car accidents 1.2 Types of crashworthiness application in space frame of car 1.3 Large deformation of passenger compartment during axial crash 1.4 Steel crash box application inspace frame of car 1.5 Large deformation of passenger compartment in side impact 1.6 Frame concept of passenger car in bending crash 1.7 Methodology of thesis 2.1 Dynamic progressive buckling 2.2 Two classes of structures 2.3 Stress-strain curves for mild steel at various uniaxial compressive strain rates 2.4 Dynamic uniaxial tensile tests on smile steel at various plastic strain rates 2.5 Variation of strength with strain rate for dynamic uniaxial tensile tests on smile steel 2.6 A typical hinge collapse mechanism 2.7 Schematic showing the bending collapse of aluminum hat profiles 2.8 Deformation pattern of fully filled beam with highly dense foam 2.9 Collapse mechanisms of box section beam 2.10 Hinge mechanism at various stages of development vii 2.11 Characteristic circles for measuring the deformation pattern 2.12 Comparison of dynamic bending moment (M)- rotation (θ) curves 2.13 Idealized stress–strain curves of elastic materials 2.14 Idealized stress–strain curves of rigid materials 2.15 Load-deflection curve for axial crushing of thin-walled column 2.16 Mean-load defection response of thin-walled column 2.17 Total energy absorption of thin-walled column 2.18 The asymmetric collapse mode of square box and basic collapse element (Type I) 2.19 Basic element type symmetric collapse element and development of part of the basic collapse element 3.1 Description of the dynamic loading case: initial and constant velocity 3.2 INSTRON 4484/ Split Hopkinson bar for tensile test 3.3 True stress– plastic strains of mild steel-St37 3.4 Typical finite element models of the thin-walled square tubes 3.5 Effect of shell elemet on the crushing respone of square tube without trigger mechanism in symmetric collapse (extensional mode) 3.6 Comparison on the crushing respone of square tube in case I and case II crashing 3.7 Effect of initial velocity on the crushing respone of square tube without trigger mechanism in asymmetric collapse (extensional mode) viii 3.8 Effect of initial velocity on the crushing respone of square tube without trigger mechanism in symmetric collapse (in-extensional mode) 3.9 Effect of wall thickness on the mean crushing force-Pm of square tube without trigger mechanism in symmetric collapse 3.10 Thin-walled square tubes has pure asymmetric as wall thickness increase 3.11 Local folding of square tubes in within and without trigger 3.12 Folding pattern Comparison between without and within trigger 3.13 Effect of trigger mechnism on the crushing respone of square tube with wall thickness t =1.14 Yield stress at various strain rate of mild steel 3.15 Effect of strain rate on the peak force of square tube with wall thickness t =1.16 Effect of strain rate on the mean crushing force- Pm of square tube with wall thickness t =1.17 Peak force-Ppeak with strain rate = 4500/s: (a) without trigger (extensional mode) and (b) with trigger (in-extensional mode), t =1.18 Mean crushing force- Pm between extensional and in-extensional mode of square tube with wall thickness t =1.5 mm at strain rate =4500/s 3.19 Mean crushing force- Pm of square tube with wall thickness t =1.5 mm at V = 20 m/s, 30 m/s, 40 m/s and 50 m/s with strain rate up to 100/s and 4500/s (extensional mode) 3.20 Mean crushing force- Pm comparision between numerical anad analytical method with wall thickness t =1.5 mm and strain rate up to 4500/s (extensional mode) ix 3.21 Mean crushing force- Pm comparision between numerical anad analytical method with wall thickness t =1.5 mm and strain rate up to 4500/s (in- extensional mode) 3.22 Progressive buckling comparison between asymmetric and symmetric collapse mode 3.23 Specific energy absorption with strain rate up to 100/s and 4500/s 4.1 Bending collapse mode of a thin-walled beam 4.2 Finite element model of a thin-walled square beam 4.3 Velocity profile of the punch during static bending process 4.4 Tensile test speciment to define stress- strain behavior 4.5 Tensile test specimen before and after do tensilte test 4.6 True stress- Plastic strain of high strength steel CR-CHSP420Y 4.7 Experimental set up for three poin bending test at MIDC (static) 4.8 Comparison between max, mean and minimum propeties of high strength steel CR-CHSP420Y to test data 4.9 Deformation geometry and friction of the beam 4.10 Punch force- displacement response for various coefficient friction 4.11 Moment-rotation response at the center length for various coefficient friction 4.