- HOME >
- BOOKLIST >
- Natural sciences>
**Solid Dynamics**

##
Solid Dynamics
*Fundamental studies on dynamic friction, impact and fracture*

#### Introduction

This book discusses solid dynamics with energy dissipation characteristics based on fundamental studies of friction, impact and fracture. Friction is one of the most significant physical phenomena in daily life, and has thus been widely studied since ancient times. The force of static friction is given by *F* = *μN*, where *μ* is the coefficient of friction and *N* is the contact force at the interface. However, many aspects of dynamic friction are still not well understood. This book presents fundamental studies on dynamic sliding friction based on experimental and model analyses, and demonstrates a number of findings. First, the sliding friction force in the dynamic case can be given by *F _{d}* =

*λAv*, where

*λ*is a parameter related to the surface condition,

*A*is the contact area, and

*v*is the sliding velocity. Second, stick-slip motion on flat surfaces can be represented by a mass-spring system with a dashpot with damping constant

*c*(=

*λA*). Third, the plowing force due to hard conical asperities on soft surfaces is given by

*P*=

_{f}*λ’A’v*, where

*λ’*is a parameter associated with the surface condition of the asperities,

*A’*is the plowing cross-sectional area, and

*v*is the sliding velocity of the asperities; the damping factor

*c*(=

_{p}*λ’A’*) influences stick-slip motion during the plowing process.

Friction also plays an important role in oblique impacts. This book describes the effect of friction on the impact of golf balls. First, the impact behavior is studied using high-speed video, and the spin or angular velocity *ω* of the ball during impact is determined. The contact area of the ball is also determined, using a rigid transparent target. Second, the effect of friction on *ω* is described, assuming that *F* = *μN* + *μη’dA*/*dt*, where *η’* is a coefficient associated with the contact surface and *dA*/*dt* is the time derivative of the contact area *A*. The friction effect is also derived using *F _{d}* =

*λAv*, where

*λAv*is qualitatively equivalent to the empirical relationship

*μN*+

*μη’dA*/

*dt*. Third, the friction-induced shear vibration of the ball can be predicted by an elastic sphere model given by

*F*=

_{d}*λAv*.

Similar to sliding friction, dynamic fracture is also a representative feature of solid dynamics with energy dissipation characteristics. A crack tip in brittle materials propagates dynamically and exhibits crack branching or arresting according to the crack acceleration or deceleration. This phenomenon is qualitatively in accord with stick-slip friction. This book investigates dynamic crack propagation using the method of caustics and a high-speed camera. First, the stress intensity factor *K _{d}* for the dynamic case is evaluated and correlated with crack velocity a ? and acceleration a ?. Second, these parameters are correlated with the change in roughness of the fracture surfaces. Crack branching is also studied to understand the energy dissipation. Third, the relationship between

*K*and a ? is examined based on the unloading rate of the specimen during crack propagation. Different specimen geometries and loading methods are used to clarify the effect of solid dynamics.

_{d}#### Contents

**Chapter 1. Introduction**

**Chapter 2. Dynamic sliding, stick-slip, and plowing friction**

2.1. Sliding of rubbers on oiled inclines

2.2. Sliding of PTFEs on dry inclines

2.3. Sliding of pencil leads on dry and oiled inclines

2.4. Stick-slip friction of rubbers on oiled surfaces

2.5. Stick-slip friction of pencil leads on dry surfaces

2.6. Plowing friction due to hard conical asperities

2.7. Plowing stick-slip friction of hard conical asperities

Appendix

References

**Chapter 3. Effect of friction on oblique impact**

3.1. Oblique impact of golf balls

3.2. Friction between ball and target

3.3. Effect of contact area on impact

3.4. Effect of friction on ball rotations

3.5. Effect of friction on shear vibrations

References

**Chapter 4. Dynamic crack propagation in solids**

4.1. Dynamic stress intensity factor

4.2. Fracture surface morphology

4.3. Crack branching criterion

4.4. Unloading behavior and crack propagation

4.5. Effects of specimen geometry and loading method

References

Index

#### Author

**Kazuo Arakawa**

K. Arakawa is a professor emeritus of Kyushu University from 2019. He received his Ph.D. from Osaka University in 1982. He became a research associate at the Research Institute for Applied Mechanics (RIAM) of Kyushu University in 1982, a visiting researcher at the University of Washington from 1988 to 1989. He was promoted to an associate professor at RIAM in 1989, and a full professor in 2001.