Influence of contact interface morphology on the nonlinear interaction between a longitudinal wave and a contact interface with friction : A numerical study
Introduction
The evaluation of damage at an early stage of fracture is relevant in many industrial applications such as aeronautics or nuclear plants. Ultrasonic methods based on linear wave scattering are efficient for detecting defects and for characterizing material elasticity, but are less sensitive to micro-cracks or closed cracks. In this context, nonlinear acoustics constitutes a good alternative for detection and evaluation of these defects, taking advantages of the nonlinear behavior of contact dynamics induced by an acoustic wave if its amplitude activates sufficiently nonlinear contact behavior.
When elastic waves and contact interfaces interact, specific nonlinear acoustic phenomena can be observed [1]: DC-effect, subharmonics generation or hysteresis/storage effects, etc. These non-classical effects are due to complex contact behavior: an asymmetrical normal stiffness, the presence of asperities and multiphysical interactions on contact surfaces that result in specific contact acoustic nonlinearity (CAN). In order to exploit these nonlinear effects it is essential to understand the complex interactions between waves and contact interfaces, and this can be achieved using analytical and numerical models. As it is not possible to include the whole complexity of contact interfaces in a model, the contact effects and study methodology have to be carefully chosen according to the objectives of the study.
Previous studies have investigated the effect of contact nonlinearity on nonlinear acoustic signatures by considering phenomenological contact models [2], [3], [4]. They lead to a mean stress/strain relation that is able to describe the observed nonlinear behavior. The advantage of these approaches is that observed behavior can be described, however they do not make it possible to understand the physical behavior of interfaces. Other approaches, called the “physical models”, based on physical contact behavior have been used to investigate the nonlinear interaction of waves and contact interfaces [5], [6]. Aleshin et al. included the influence of asperities on nonlinear acoustics [7], [8], in a model based on memory-diagrams which has been implemented in a Finite Element (FE) code.
Richardson [9] provides an analytical study of the interaction between a longitudinal plane wave (therefore infinite) and an infinite contact interface between two identical media considering a unilateral contact law. It corresponds to an infinitely rigid contact that cannot support tension and hence opens up in the tension phase [9]. In the case of an incident sinusoidal wave, second harmonic generation efficiency (which corresponds to the ratio of the second harmonic to the incident wave amplitude) can be determined, and shows a specific nonlinear signature. Based on this work, other studies aimed at explaining the relation between contact nonlinearity and harmonic evolution considering an interface [10], [11], [12], [13] or a crack [6]. They show that nonlinear signatures provide some information on interface parameters (contact stresses, friction induced energy dissipation, crack orientation, etc.) if they are measurable. These studies take into account both the “clapping” effect and sliding with friction on a perfectly plane interface. They give a good understanding of interactions between wave and contact in a model case, but do not take into account asperities and non-conforming profiles that actually exists in the case of real cracks and that can play an important role during dynamic interactions with waves.
Including asperities in the model leads to difficulties of interpretation if too many parameters are involved. For example, in [7], the contact model introduces a nonlinear normal contact stiffness in compression, and consequently other effects are introduced during the interactions between waves and contact interfaces that, as far as we know, are not fully analyzed and understood. The present paper considered non-conforming profile interface between two deformable solids. A unilateral contact law with Coulomb’s friction is applied locally in order to investigate the effect of the coexistence of open and closed zones in the interaction zone. This is physical approaches to contact modeling. If it does not take into account a large number of contact effects (adhesion, asperities, contact stiffness, wear), but it describes interface closing/opening (“clapping” effect) and sliding with friction (“sliding” effect) with only one parameter: the friction coefficient. In the first part of the paper, a 1D model of the nonlinear interaction between a plane wave and an infinite interface is used to analyze second harmonic evolution as a function of pre-stress and incident wave magnitude in the cases of closed and open contact interfaces. Next, the experimental results of second harmonic evolution as a function of applied stress on a real crack are presented. In the third part, the effect of the coexistence of closed and open parts within the interaction zone on second harmonic generation is investigated numerically using a 2D-FE model. Investigation of local contact behavior in relation to local harmonic generation is a way to go further in the evaluation of cracks and contact interfaces.
Section snippets
1D-Numerical study of a longitudinal wave reflected from a unilateral contact interface
In this part, a homogeneous, isotropic elastic half-space defined as is assumed to be in perfect contact with a rigid wall on a line at . The half-space and the rigid plane are brought into contact under a given compression normal stress () or maintained open with a normal initial displacement gap () (Fig. 1). An incident plane longitudinal wave is generated at and propagates linearly in in the positive -direction with a velocity (approximately 6000 m.s−1 in
Experimental evidence of different evolutions of the second harmonic for a real fatigue crack
In this section, experimental results are presented for the second harmonic generation of a real fatigue crack. The experimental set-up and cracked sample are shown in Fig. 4(a) and (b) respectively. Compression force loading is applied to the sample using a threaded rod and nuts. This force is monitored through a load-cell located between the screw thread and the sample. In practice the system is mounted horizontally to allow the application of loads lower than the sample weight. A 32 mm
2D-Numerical study of a longitudinal wave interacting with contact interfaces of different morphologies
Two configurations (Fig. 7) are considered both including two steel blocks in contact. They differ in their contact interface morphologies. The first configuration (Fig. 7(a)) consists in a perfectly plane contact interface, while the second involves an interface between a concave surface and a plane surface (Fig. 7(b)). For the plane interface, the normal applied force will result in a quasi-uniform pre-stress. In this case, the interface will remain closed whatever the applied force.
Local analysis of contact acoustic nonlinearity and harmonic generation
In this part, a local analysis of CAN is proposed through local dimensionless parameters and along a contact interface defined as: where and correspond to maximal values of incident stress and displacement respectively. These parameters are dependent on as the incident wave is non-plane (Fig. 9), and the pre-stress and initial normal gap are non-uniform in the concave case (Fig. 8). In the case of a plane
Conclusion
In this paper, the interaction of a longitudinal wave and a unilateral contact interface has been analyzed. First, a 1D analysis was carried out to retrieve evolutions of the second harmonic as a function of the dimensionless parameters and already described in the literature. These evolutions were compared to some experimental results in a sample with a real crack for different transmitter and receiver positions. These results motivated a 2-D FE analysis considering two blocks in contact
CRediT authorship contribution statement
Abdelkrim Saidoun: Conception and design of study, Acquisition of data, Analysis and/or interpretation of data, Writing - review & editing. Anissa Meziane: Conception and design of study, Acquisition of data, Analysis and/or interpretation of data, Writing - original draft, Writing - review & editing. Mathieu Renier: Conception and design of study, Acquisition of data, Analysis and/or interpretation of data, Writing - review & editing. Fan Zhang: Analysis and/or interpretation of data, Writing
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
The authors would like to thank Fondation CETIM for their support. Approval of the version of the manuscript to be published.
References (17)
- et al.
CAN: an example of nonclassical acoustic nonlinearity in solids
Ultrasonics
(2002) - et al.
Numerical simulation of Rayleigh wave interaction with surface closed cracks under external pressure
Wave Motion
(2015) - et al.
Numerical study of nonlinear interaction between a crack and elastic waves under an oblique incidence
Wave Motion
(2014) - et al.
Two dimensional modeling of elastic wave propagation in solids containing cracks with rough surfaces and friction, Part I: Theoretical background
Ultrasonics
(2018) - et al.
Two dimensional modeling of elastic wave propagation in solids containing cracks with rough surfaces and friction, Part II: Numerical implementation
Ultrasonics
(2018) Harmonic generation at an unbonded interface - I Planar interface between semi-infinite elastic media
Internat. J. Engrg. Sci.
(1979)- et al.
Time reversal invariance for a one-dimensional model of contact acoustic nonlinearity
J. Sound Vib.
(2017) The non-smooth contact dynamics method
Comput. Methods Appl. Mech. Engrg.
(1999)
Cited by (4)
Combined harmonic generation of feature guided waves mixing in a welded joint
2023, Wave MotionCitation Excerpt :Nevertheless, when it comes to damage at the early stage, i.e., inceptive fatigue crack (namely the crack size is smaller in several orders of wavelength), the sensitivity of linear ultrasonic techniques is insufficient [2]. The unique sensitivity of nonlinear ultrasonic waves to micro-defects has been demonstrated to have the potential to detect microscopic defects in materials [3–5]. Nonlinear guided wave, which combines the high sensitivity of nonlinear ultrasonic waves to damage in microscale with the distinct advantages of the guided wave, has intrigued extensive researchers to investigate how to fulfill its potential to detect incipient damage in large structures [6–8].
Embedded PZT aggregates for monitoring crack growth and predicting surface crack in reinforced concrete beam
2023, Construction and Building MaterialsCitation Excerpt :Moreover, the sensor energy is greater than zero because some stress waves as transmitted waves pass through the micro-crack. Whether the micro-crack is closed depends on whether the displacement at the crack’s left surface is greater than the crack gap’s width [40,41]. Before the crack is closed, the inclined incident elastic P-wave produces reflected P-wave and S-wave at the left surface of the crack and no transmission waves are generated.
Advances in nonlinear ultrasonic detection of microcracks
2022, Kexue Tongbao/Chinese Science Bulletin