#### Location

La Jolla, CA

#### Start Date

1-1-1991 12:00 AM

#### Description

The elastic behavior of a solid consists of linear and nonlinear contributions. The linear part is represented by the well known Hooke’s law which is given in tensorial notation as (1) σij=Cijklεkl where σij and εkl are the stress and strain tensors, respectively, and Cijkl is the tensor of the second order elastic constants (SOEC). This relationship is sufficient for many engineering calculations since deviations from a purely linear elastic behavior are small. Hooke’s law, however, is not sufficient for an advanced characterization of the elastic behavior of materials. This is due to the fact that many of the physical and mechanical properties of materials are of nonlinear nature. The nonlinear elastic behavior can be investigated using ultrasonic techniques because of their high sensitivity for small nonlinear effects. Among the nonlinear effects are the stress and the temperature dependences of ultrasonic velocities in the solid. These effects have gained considerable interest in the last decade, particularly for the nondestructive evaluation of applied and residual stresses [1], and also for the microstructural characterization of materials [2]. Another physical manifestation of the nonlinear elastic behavior of solids is the acoustic nonlinearity parameter. This parameter can be determined from measurements of the amplitudes of fundamental and second harmonic when an originally sinusoidal wave gets distorted while propagating through the solid. The nonlinearity parameter can also be calculated from a combination of second and third order elastic constants. In previous studies [3], the nonlinearity parameter was found to be sensitive to microstructural changes in aluminum alloys and in particular to the content of precipitates of the second phase.

#### Book Title

Review of Progress in Quantitative Nondestructive Evaluation

#### Volume

10B

#### Chapter

Chapter 7: Characterization of Materials

#### Section

Non-Linear Acoustic Properties

#### Pages

1821-1828

#### DOI

10.1007/978-1-4615-3742-7_89

#### Copyright Owner

Springer-Verlag US

#### Copyright Date

January 1991

#### Language

en

#### File Format

application/pdf

Acoustic Nonlinearity in Metal — Matrix Composites

La Jolla, CA

The elastic behavior of a solid consists of linear and nonlinear contributions. The linear part is represented by the well known Hooke’s law which is given in tensorial notation as (1) σij=Cijklεkl where σij and εkl are the stress and strain tensors, respectively, and Cijkl is the tensor of the second order elastic constants (SOEC). This relationship is sufficient for many engineering calculations since deviations from a purely linear elastic behavior are small. Hooke’s law, however, is not sufficient for an advanced characterization of the elastic behavior of materials. This is due to the fact that many of the physical and mechanical properties of materials are of nonlinear nature. The nonlinear elastic behavior can be investigated using ultrasonic techniques because of their high sensitivity for small nonlinear effects. Among the nonlinear effects are the stress and the temperature dependences of ultrasonic velocities in the solid. These effects have gained considerable interest in the last decade, particularly for the nondestructive evaluation of applied and residual stresses [1], and also for the microstructural characterization of materials [2]. Another physical manifestation of the nonlinear elastic behavior of solids is the acoustic nonlinearity parameter. This parameter can be determined from measurements of the amplitudes of fundamental and second harmonic when an originally sinusoidal wave gets distorted while propagating through the solid. The nonlinearity parameter can also be calculated from a combination of second and third order elastic constants. In previous studies [3], the nonlinearity parameter was found to be sensitive to microstructural changes in aluminum alloys and in particular to the content of precipitates of the second phase.