• 비파괴검사학회지
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• 제33권3호
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• pp.276-282
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• 2013

This paper proposes an ultrasonic method for measurement of linear and hysteretic interfacial stiffness of contacting surfaces between two steel plates subjected to nominal compression pressure. Interfacial stiffness was evaluated by the reflection and transmission coefficients obtained from three consecutive reflection waves from solid-solid surface using the shear wave. A nonlinear hysteretic spring model was proposed and used to define the quantitative interfacial stiffness of interface with the reflection and transmission coefficients. Acoustic model for 1-D wave propagation across interfaces is developed to formulate the reflection and transmission waves and to determine the linear and nonlinear hysteretic interfacial stiffness. Two identical plates are put together to form a contacting surface and pressed by bolt-fastening to measure interfacial stiffness at different states of contact pressure. It is found from experiment that the linear and hysteretic interfacial stiffness are successfully determined by the reflection and transmission coefficient at the contact surfaces through ultrasonic pulse-echo measurement.

• 비파괴검사학회지
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• 제30권6호
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• pp.578-586
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• 2010

This paper describes a theoretical model and acoustic analysis of hysteresis of contacting surfaces subject to compression pressure. Contacting surfaces known to be nonlinear and hysteretic is considered as a simple spring that has a complex stiffness connecting discontinuous displacements between two solid contact boundaries. Mathematical formulation for 1-D interfacial wave propagation between two contacting solids is developed using the complex spring model to derive the dispersion relation between the interface wave speed and the complex interfacial stiffness. Existence of the interface wave propagating along the hysteretic interface is studied in theory and discussed by investigating the solution to the dispersion equation. Unlike the linear interface without hysteresis, there can exist only one distinct mode of interface waves for the hysteretic interface, which is anti-symmetric motion. The anti-symmetric mode of interface wave propagates with the velocity faster than the Rayleigh surface wave but less than the shear wave depending on the interfacial stiffness. If the contacting surfaces are compressed so much that the linear interfacial stiffness is very high, the hysteretic stiffness does not affect the interface wave velocity. However, it has an effect on the speed of interface wave for a loosely contact surfaces with a relatively low linear stiffness. It is also found that the phase velocity of anti-symmetric wave mode converges to the shear wave velocity in despite of the linear stiffness value if the hysteretic stiffness approaches 0.5.

• Interaction and multiscale mechanics
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• 제1권2호
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• pp.279-301
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• 2008

This paper develops a 3D homogenization based continuum damage mechanics (HCDM) model for fiber reinforced composites undergoing micromechanical damage under monotonic and cyclic loading. Micromechanical damage in a representative volume element (RVE) of the material occurs by fiber-matrix interfacial debonding, which is incorporated in the model through a hysteretic bilinear cohesive zone model. The proposed model expresses a damage evolution surface in the strain space in the principal damage coordinate system or PDCS. PDCS enables the model to account for the effect of non-proportional load history. The loading/unloading criterion during cyclic loading is based on the scalar product of the strain increment and the normal to the damage surface in strain space. The material constitutive law involves a fourth order orthotropic tensor with stiffness characterized as a macroscopic internal variable. Three dimensional damage in composites is accounted for through functional forms of the fourth order damage tensor in terms of components of macroscopic strain and elastic stiffness tensors. The HCDM model parameters are calibrated from homogenization of micromechanical solutions of the RVE for a few representative strain histories. The proposed model is validated by comparing results of the HCDM model with pure micromechanical analysis results followed by homogenization. Finally, the potential of HCDM model as a design tool is demonstrated through macro-micro analysis of monotonic and cyclic damage progression in composite structures.