Impact Dynamics

1. Impact Dynamics 撞擊力學

2. 大葉大學94學年度 第2學期 機械工程研究所碩士班1年1班系課程綱要

3. 大葉大學94學年度 第2學期 機械工程研究所碩士班1年1班系課程綱要 (續)

4. 大葉大學94學年度 第2學期 機械工程研究所碩士班1年1班系課程綱要 (續)

5. 大葉大學94學年度 第2學期 機械工程研究所碩士班1年1班系課程綱要 (續)

6. 大葉大學94學年度 第2學期 機械工程研究所碩士班1年1班系課程綱要 (續)

7. 大葉大學94學年度 第2學期 機械工程研究所碩士班1年1班系課程綱要 (續)

8. 大葉大學94學年度 第2學期 機械工程研究所碩士班1年1班系課程綱要 (續)

9. Introduction

10. Introduction Kinetics

11. Introduction

12. Introduction Impact Dynamics • Situations involving impact–the collision of two or more solid–are currently receiving widespread attention. • At one time, impact problems were primarily of concern to military. • Now however, as civilian technology grows more sophisticated, severe demands are being made on the behavior of materials under very short duration loading. • Safe and cost-effective design demands a rigorous understanding of the behavior of material and structures subjected to intense impulsive loading for such diverse applications as: 1. Safe demolition of prestressed concrete structures. 2. The transportation safety of hazardous materials. 3. Crashworthiness of vehicles and protection of their occupants or cargo. 4. Safety of nuclear-reactor containment vessels subjected to missile impact from external sources or internal ones. 5. The design of lightweight armor systems, including fabric body armors, for protection of police officers, executives in business, and government and military personnel. 6. The vulnerability of military vehicles, aircraft, and structures to impact and explosive loading. 7. The erosion and fracture of solids subjected to multiple impacts by liquid and solid particles. 8. Protection of spacecraft from meteroid impact. 9. Explosive forming and welding of metals.

13. Introduction

14. Introduction Impact Velocity

15. Introduction • The study of impact phenomena involves a variety of classical disciplines. In the low–velocity regime (<250 m/s) many problems fall in the area of structural dynamics. • Local indentations or penetrations are strongly coupled to the overall deformation of structure. Typically, loading and response times are in the millisecond regime. • As the striking velocity increases (0.5-2km/s) the response of the structure becomes secondary to the behavior of the material within a small zone (typically 2-3 projectile diameters) of the impact area. • A ware description of the phenomena is appropriate and the influences of velocity, geometry, material constitution, strain rate, localized plastic flow, and failure are manifest at various stages of the impact process. • Typically, loading and reaction times are on the order of microseconds. • Still further increases in impact velocity (2-3km/s) result in localized pressures that exceed the strength of the material by an order of magnitude. in effect, the colliding solids can be treated as fluids in the early stages of impact. • At ultra-high velocities (>12km/s) energy deposition occurs at such a high rate that an explosive vaporization of colliding materials results.

16. Introduction • Impact phenomena can be characterized in a number of ways: according to the impact angle, the geometric and material characteristics of the target or projectile, or striking velocity. • The latter approach is adopted in Table, which provides a short classification of impact processes as a function of striking velocity, Vs, and strain rate, . • The impact-velocity ranges should be considered only as reference point. In fact, these transitions are extraordinarily flexible since deformation processes under impact loading depend on a long series of parameters in addition to impact velocity. • A complete description of the dynamics of impacting solids would demand that account be taken of the geometry of the interacting bodies, elastic, plastic, and shock-ware propagation, hydrodynamicflow, finite strains and deformations, work hardening, thermal and frictional effects, and the initiation and propagation of failure in the colliding materials. .

17. Introduction • An analytical approachwould not only be quite formidable, but would also require a degree of material characterization under high strain-rate loading that could not be attained in practice. • Hence, much of the work in this field has been experimental in nature. • Penetration may be defined as the entrance of a missile into a target without completing its passage through the body [Backman and Goldsmith (1978)]. This generally results in the embedment of the striker and formation of a crater. • If the projectile rebounds from the impacted surface or penetrates along a curved trajectory emerging through the impacted surface with a reduced velocity, the process is termed aricochet. • Perforation, in contrast, is the complete piercing of a target by the projectile. Such processes occur in a time frame of several to several hundred microseconds. Targets and projectiles are usually severely deformed during such encounters.

18. Introduction

26. Mathematical Description of Material Behavior • The most general from of a material-constitutive equation should cover the description of material behavior under the total range of the strain rates that may be encountered. • However, this can be extremely difficult, even for uniaxial stress, and therefore the majority of constitutive equations generally cover only a narrow range of strain rates. • This is not inconsistent with the physics of the problem, since different mechanisms govern the deformation behavior of materials within different strain-rate regimes. • Some of the considerations in dynamic testing have been summarized by Lindholm (1971) as shown in Figure. • At strain rates of the order of 10‑6 to 10-5 s-1 the creep behavior of a material is the primary consideration, usually at elevated temperatures for metals, and creep-type laws are used to describe the mechanical behavior. • At higher rate, in the range 10‑4 to 10-3 s-1, the uniaxial tension, compression, or quasistatic stress-strain curve obtained from constant strain-rate tests is used to describe the material behavior.

27. Mathematical Description of Material Behavior • Although the quasistatic stress-strain curve is often treated as an inherent property of a material, it is a valid description of the material only at the strain rate at which the test was conducted. • As higher strain rates are encountered, the stress-strain properties may change, and alternate testing techniques have to be employed. Constant strain-rate tests can be performed with specialized testing apparatus at strain rates up to approximately 104s-1. • The range of strain rates from 10‑1 to 102s-1 is generally referred to as the intermediate or medium strain-rate regime. It is within this regime that strain-rate effects first become a consideration n most metals, although the magnitude of such effects may be quite small or even nonexistent in some cases. • Strain rates of 103 s-1 or higher are generally treated as the range of high strain-rate response, although there are no precise definitions as to strain-rate regime and care must be taken in evaluating data to note the actual strain rates rather than the terminology.

28. Mathematical Description of Material Behavior ． ε -4 10

29. Mathematical Description of Material Behavior

30. Mathematical Description of Material Behavior • Impact dynamics has two features which distinguish it from the more conventional disciplines of the classical mechanics of rigid or deformable bodies under quasi-static conditions. • The first is the importance of inertia effects which must be considered in all of the governing equations based on the fundamental conservation laws of mechanics and physics. • The second is the role of stress wave propagation in the analysis of problems and the recognition that most impact events are transient phenomena where steady-state conditions do not exist. In this introduction to the subject, both aspects of the problem are summarized. • Solutions to impact problems can take any one of three separate forms. • The first is the purely empirical approach where large amounts of experimental data are obtained and correlated. While this is a useful procedure for solving a specific problem, it is difficult and dangerous to extrapolate the information to other materials or geometries outside the velocity range of the tests. This approach provides little if any fundamental understanding of material behavior or the underlying mechanism behind the impact event.

31. Mathematical Description of Material Behavior • The second approach is the development and use of engineering models to simulate impact events. Usually, these models are base on the combined application of the fundamental conservation laws and insights and assumptions painting to the deformation or failure processes gained from prior observations. This approach can range anywhere in sophistication from a simple one-dimensional penetration model based on a single mechanism to more complex two- and three-dimensional models based on a combination of mechanisms and assumed deformation fields. • It is sometimes difficult to distinguish the first and second approaches in the literature because there can be overlap in the methods used. The terms model and correlative equation are often used interchangeable; many empirical observations and curve-fitting schemes are referred to as models. • The third approach to solving impact problems is the discretization method whereby the structure of the impacting bodies is broken up into small elements and the fundamental laws of physics are applied to each element. • Although the use of proper numerical techniques provides accurate solutions to complex problems through finite element or finite differenceprocedures, the approach is computationally time consuming and limited to single problem since the entire numerical procedure must be repeated for any changein input variables. In addition, the solution is no more accurate than the description of material deformation and failure behavior.

32. Mathematical Description of Material Behavior • Each of the three procedures for solving impact problems has it own merits and disadvantages. Since one or two procedures cannot always provide all the desired information concerning a complex impact phenomenon, a combination of all three is often the best approach. • For example, the empirical approach can be used to deduce the general modes of deformation and failure over given ranges of test variables and provide observational modeling insights. • Numerical modeling can be used to determine details of deformation and stress fields. • These pieces of information can then be used to verify and improve engineering models for impact events. • Successful application of these procedures depends upon an understanding of the related basic principles. • The basic principles which pertain include the conservation laws, the role of ware propagation, the influence of inertia, and an understanding of material behavior under high rates of loading. • This latter aspect is an integral part of all studied of high velocity impact dynamics. Because of the short time duration involved in impact phenomena, the response of the materials involved influences the impact event. • Therefore, the study of impact requires the study of dynamic behavior of materials. For an example of the role of material behavior in an impact event, the reader is referred to the state-of-the-art assessment presented in a 1980 National Materials Advisory Board committee report (NMAB, 1980). Various aspects of material behavior are summarized in a series of review articles in Chou and Hopkins (1972).

33. Primary goals of vehicle crash mechanics • This textbook, Vehicle Crash Mechanics, has grown out of a series of Matthew Huang lectures on vehicle crashworthiness at the University of Michigan, Dearborn. Since 1991, these lectures have been presented to automotive engineers from the Ford Motor Company, full service suppliers to the Ford Motor Company, and engineers from various consulting firms. • The primary goals of this course are to provide the fundamentals of engineering mechanics and to apply these fundamentals to the study of vehicle crashworthiness. Also the book was written to present a number of interesting and ancillary topics related to vehicle crashes but extending beyond purely fundamental theory. • In the automotive-related industry, the goal of engineering effort in the field of crashworthiness is to satisfy, or, to the extent possible, exceed the safety requirements mandated by the Federal Motor Vehicle Safety Standars (FMVSS) and administered by the National Highway Traffic Safety Administration (NHTSA). • Governed as it is by strict adherence to regulations and the balancing of complex interactions among the variables, the application of mechanics to crashworthiness is not a simple task. The importance of understanding the fundamentals of mechanics cannot be overemphasized. In this book, I have strived to present the fundamentals as clearly as possible, and with an aim toward applications to problems.

34. Primary goals of vehicle crash mechanics • This field can be subdivided in to four groups: (1) Vehicle crash dynamics, (2) Computer aided engineering, (3) Occupant impact dynamics, and (4) Design analysis and accident reconstruction. In each of these groups, knowledge of the fundamental principles mechanics is essential. Also, the ability to apply such knowledge to hardware, to developmental work, or analytical modeling is required. • First, the fundamentals, which range from particles dynamics to rigid body kinetics, are presented. Then Newton’s Second Law, the principle of impulse and momentum, and the principle of work and energy are applied to engineering problems. • It is assumed that the student has had courses in mathematics through calculus and engineering statics. Formulas are presented as needed; as each one is presented for the first time, a short derivation of the formula id provided. • Through out the course, when analyzing vehicle tests, both the analysis of actual test results and the interprentation of mathematical models related to the test will be developed in parallel. • This approach is done in an orderly fashion in order to provide an insight into the parameters and interactions that influence the results. • In the study of the crashworthiness, three main elements can be defined: vehicle, occupant, and restrains (VOR). In this course, the dynamic interactions among these three elements will be illustrated by the use of analytical models, experimental methods, and test data from actual vehicle crash tests. • As an example, the occupant-vehicle kinematics in the restrain coupling phase and the use of the ride down concept are presented in both analytical and experimental terms.