Frictional contact of two spheres for arbitrary 2D loading

Frictional interaction of two elastic spheres is a fundamental problem of contact mechanics. The tangential displacement depends on the normal and tangential force in a complicated and, in general, hysteretic way. We analyze in detail the key memory characteristic of the system (the traction distribution in the contact zone) and write out analytical solutions in various loading regimes. Then, a general scheme of memory organization is established that enables to describe all possible regimes in a universal way. The result is a computer-assisted general solution to the problem

Recent advances in the ultrasonic polar scan method for characterizing (degraded) fiber reinforced plastics

The ultrasonic polar scan (UPS) technique originated in the 1980's as a sophisticated method for inspecting composites. However, it is only in recent times that the true capabilities and strengths of the UPS methodology have been evidenced through experiment and simulation. Nowadays, the UPS method exists in different versions which led to several novel applications in the field of material inspection and characterization. This contribution gives an overview of our recent advances

Ultrasonic characterization of subsurface 2D corrugation

The ultrasonic backscattering technique is employed for the characterization of a 2D surface corrugation which is superposed on or hidden on the backside of a polycarbonate sample. In contrast to previous studies where the incident angle at well-defined and a-priori known symmetry orientations of the surface structure is varied in order to extract the characteristic periodicities, the backscatter polar scan method incorporates an additional variation of the orientation of the vertical insonification plane within the experimental measurement protocol. As such, the characteristic periodicities as well as the surface symmetries can be extracted without any prior knowledge of the surface structure. As a benefit compared to optical methods, we have also validated this extended methodology for the investigation of a 2D subsurface corrugation. Although the diffraction conditions do not change in comparison with a visible 2D surface corrugation, we remark that additional attention is required in the sense that the elastic properties of the substrate material put further restrictions to the range of applicable ultrasonic frequencies. The characterized periodicities and symmetries are in excellent agreement with the design parameters of the (hidden) 2D surface grating

A novel ultrasonic strain gauge for single-sided measurement of a local 3D strain field

A novel method is introduced for the measurement of a 3D strain field by exploiting the interaction between ultrasound waves and geometrical characteristics of the insonified specimen. First, the response of obliquely incident harmonic waves to a deterministic surface roughness is utilized. Analysis of backscattered amplitudes in Bragg diffraction geometry then yields a measure for the in-plane strain field by mapping any shift in angular dependency. Secondly, the analysis of the reflection characteristics of normal incident pulsed waves in frequency domain provides a measure of the out-of-plane normal strain field component, simply by tracking any change in the stimulation condition for a thickness resonance. As such, the developed ultrasonic strain gauge yields an absolute, contactless and single-sided mapping of a local 3D strain field, in which both sample preparation and alignment procedure are needless. Results are presented for cold-rolled DC06 steel samples onto which skin passing of the work rolls is applied. The samples have been mechanically loaded, introducing plastic strain levels ranging from 2% up to 35%. The ultrasonically measured strains have been validated with various other strain measurement techniques, including manual micrometer, longitudinal and transverse mechanical extensometer and optical mono- and stereovision digital image correlation. Good agreement has been obtained between the ultrasonically determined strain values and the results of the conventional methods. As the ultrasonic strain gauge provides all three normal strain field components, it has been employed for the extraction of Lankford ratios at different applied longitudinal plastic strain levels, revealing a strain dependent plastic anisotropy of the investigated DC06 steel sheet

Time-of-flight recorded pulsed ultrasonic polar scan for elasticity characterization of composites

In its orginal configuration, the pulsed ultasonic polarscan (P-UPS) mainly focussed on elastic material characterization through the inversion of amplitude landscape measurements. However, for several materials, special attention is required as minima in the transmission amplitudes do not exactly coincide with critical angles calculated from the Christoffel equations. Consequently, other means to extract the information on elastic moduli from P-UPS measurements are being investigated. In the present paper, we report on the use of time-of-flight ultrasonic polarscan (TOF-UPS) simulations as a new means of material characterization. Previous TOF inversions, although successful, were based on bulk wave approximations, which are not longer valid for thin materials. Our first inversion results on numerical cases demonstrate the usefulness of the new developed technique and highlight the added value compared to the bulk wave approximation

Linear and nonlinear guided wave imaging of impact damage in CFRP using a probabilistic approach

The amount and variety of composite structures that need to be inspected for the presence of impact damage has grown significantly in the last few decades. In this paper, an application of a probabilistic ultrasonic guided wave imaging technique for impact damage detection in carbon fiber-reinforced polymers (CFRP) is presented. On the one hand, a linear, baseline-dependent, technique utilizing the well-known correlation-based RAPID method and an array of piezoelectric transducers is applied to detect impact-induced damage in plate-like composite structures. Furthermore, a baseline-independent nonlinear extension of the standard RAPID method is proposed, and its performance is demonstrated both numerically and experimentally. Compared to the conventional RAPID, the baseline-free version suffers from a somewhat lower imaging quality. However, this drawback is compensated by the fact that no damage-free (intact) baseline is necessary for successful imaging of damage

Matching spectroscopy with the ultrasonic polar scan for advanced NDT of composites

The Pulsed Ultrasonic Polar Scan (P-UPS) is a powerful technique for characterizing anisotropic materials like fiber reinforced plastics. A time-domain analysis of the ultrasonic signals yields amplitude and time-of-flight polar diagrams that provide a fingerprint of the local stiffness properties. Though, this simple analysis ignores a lot of information contained in the ultrasonic signals. In this study, we propose to use the P-UPS technique in combination with the spectroscopic analysis of broadband pulses, to obtain plane wave transmission spectra for all in-plane polar angles. This allows us to combine on one hand the strengths of the P-UPS technique, that does not require a priori knowledge about the sample anisotropy, and on the other hand the frequency-domain analysis that utilizes information contained in the broadband pulses