Non-Linear Aspects of Friction Material Elastic Constants

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In this report, we describe the ultrasonic measurement process applied to a series of three brake pad materials with varying degrees of load-dependent, non-linear behavior.  For each material type, we measure the spatial variation of the ultrasonic velocity and the spatial variation of ultrasonic attenuation on several, as-manufactured, brake pads. We correlate these ultrasonic test results with those obtained by conventional compressibility tests.  Subsequently, we destructively analyze each friction material. The load-dependence of the through-the-thickness longitudinal and shear velocity is measured using static loads ranging from 0.5 MPa to 8.0 MPa. For selected friction materials exhibiting significant variations in velocity with load, we compute the full set of engineering constants.  Our analysis includes computation of the Young’s modulus, shear modulus, and Poisson’s ratios as a function of load.  We discuss the sensitivity and repeatability of the methods and their application to both material formulation development and improved material uniformity.


The Noise, Vibration and Harshness (NVH) behavior of braking systems is a complex problem involving the simultaneous interaction of several materials and numerous systems design variables.  Many developers of braking systems have resorted to modeling and simulation in an effort to understand the various factors that determine performance.  As input to the noise and vibration models, accurate material property data such as the Young’s modulus, shear modulus, and Poisson’s ratio are essential. The determination of relevant elastic properties is challenging due to the use of several friction materials with material inhomogeniety, anisotropy, and non-linear properties.

Although significant progress has been made in both modeling and measurement methods, no single measurement or modeling approach is sufficiently robust to permit a priori prediction of a friction material’s performance in new braking applications.  In this paper, we discuss the ultrasonic measurement of elastic constants with an emphasis on the role of spatial variations and non-linear, load-dependent material properties.

Experimental Methods

The intent of this study is two-fold: 1) to use ultrasonic methods to carefully characterize the uniformity of as-manufactured brake pads and 2) to determine the influence of non-linear load-dependent properties on the measurement and computation of friction material engineering constants.   In contrast to laboratory methods used in destructively measuring friction material elastic constants, in this study we placed a significant effort on non-destructively measuring the properties of as-manufactured pads in order to quantify the material variability. 

Ultrasonic Methods

The use of ultrasound to determine the mechanical properties of materials is based on the fundamental relationship between the ultrasonic velocity and the material elastic constants.  These methods have been described in a number of books and review articles.1-5  A review article describing ultrasonic methods for measuring elastic constants of friction materials is given by Yuhas & Yuhas.6

The ultrasonic technique used in this study is an ultrasonic through thickness transmission technique.  The basic concept of ultrasonic testing is illustrated in Figure 1. A short burst of high frequency sound (typically 1 MHz to 3 MHz) is generated from the transmitting transducer and propagates through the sample to the receiving transducer. Measurements are made of the transit time using the ultrasonic signal that is digitized at a rate of 50 MHz. Thus, a transit time precision of 20 nanoseconds can be achieved. If the thickness is known, the ultrasonic velocity can be determined from the transit time measurement.  By measuring velocities of shear and longitudinal wave modes for different sample orientations, the material elastic constants can be determined.  In order to efficiently couple the ultrasound to the sample, a viscous liquid coupling gel is used.

Figure 1
Figure 1 Basic ultrasonic data collection geometry

In contrast to other measurements, (e.g. resonance or compressibility) ultrasonic velocity measurements are highly localized. This represents both one of the strengths and one of the weaknesses of this method.  For inhomogeneous materials, it may be necessary to sample several areas in order to obtain a representative estimate of the pad properties.  In contrast to previous ultrasonic studies where measurements were only made on friction material samples extracted from the intact brakes, in this report all samples were initially analyzed in the as-manufactured condition.

For our experiments, we use a 12.5 millimeter diameter transducer which defines the lateral extent of the probing field.  For the longitudinal waves, data is taken using an ultrasonic frequency of 1 MHz.  For shear waves we use a frequency of 2.25 MHz.  All measurements are made in transmission so the beam interrogates the volume of the full thickness of the pad covered by the surface area of the transducer (1.22 sq. cm). 

In addition to measuring the ultrasonic velocity, we also generated ultrasonic images of intact pads.  For the images, only the signal loss is measured.  Unlike the velocity, the signal loss is not fundamentally related to the elastic constants.  However, the signal transmission is sensitive to local porosity, fiber/matrix bonding, and the bond integrity of the friction material/steel backing bond.  For the ultrasonic images, the samples were immersed in a water bath which provided the coupling to the sample.  This data provides a qualitative visual measure of material uniformity.


The compressibility of all pads investigated in this study was measured in accordance with SAE specification J2468.  We report the absolute reduction in thickness for line pressure of 100 bar.  All measurements were conducted at room temperature.


Three different passenger car brake pads were used for this investigation.  The materials were chosen in order to obtain a range of nonlinear load dependent behavior. Our test set includes 2 high performance friction materials, HP-1 & HP-2, and one semi-metallic formulation SM-1.  For each group, 6 pads were analyzed.  The material formulation within each group is the same.  However, HP-1 was sub-grouped into HP-1a and HP-1b.  Although the friction formulation was the same within this group some aspects of the processing and the under-layer material differ.  Each material group has a different pad geometry or “form factor”.

As-manufactured “Intact” Pads

Spatial Variation

In terms of their elastic properties, friction materials have transversely isotropic symmetry.  Thus, in order to properly interpret the ultrasonic data, it is necessary to define a coordinate system relative to the brake pad.  The coordinate system used for our study is illustrated in Figure 2 where the unique axis of our transversely isotropic solid is in the “3” direction (through-the-thickness).  The friction materials are isotropic in the plane of the pad, “1” and “2” directions in Figure 2. This transverse isotropy is confirmed by the similarity of measured ultrasonic velocity for the in-plane longitudinal modes, V11 = V22.  For intact pads 4 velocity modes can be measured.  This includes two in-plane modes V22 and V21 and two through-the-thickness modes V33 and V32.  In order to measure the uniformity of the pads we made multiple measurements of the V33 and V32 modes.  The V33 mode is a longitudinal wave propagated through-the-thickness of the pad, while the V32 mode is a shear wave propagating through-the-thickness of the pad.

Figure 2
Figure 2 Coordinate definition referenced to a typical disk pad

The V33 mode is related to the C33 diagonal element of the elastic constant matrix by the formula C33 = r(V33)2 where r is the density. Thus, the value of V33 is related to the stiffness in the through-the-thickness, “3” direction.  The V32 mode is a shear wave mode and is related to the C44 elastic constant by the formula C44 = r(V32)2.

For each pad, multiple locations were measured. In some pads, seven measurements were made while in others only five measurements were made of each mode.  In all cases, a force of 890 N (200 lbs) was used to couple the transducers to the friction material.  A viscous, organic coupling compound, (IMS-SWC), was used to promote ultrasonic transmission.

In general, in order to make a meaningful measurement of the ultrasonic velocity, it is necessary to have flat and parallel entrance and exit areas for the ultrasonic beam.  For those pads that have holes in the steel backing plate, it is necessary to avoid these zones and thus they are excluded from the measurement process.

The measurement process begins with generating a scanning template which is illustrated in Figure 3. In this case, we measure seven locations in each pad as indicated by the numbered circles in Figure 3. The smaller, shaded circles indicate the steel backing through holes.  Each measurement area is 12.5 millimeters in diameter.  As can be seen from the diagram, positions 1 and 7 represent the leading and trailing edges of the pad, positions 3, 4, and 5 are all located on the inner radius and the other positions 1, 2, 6, and 7 are on the outer pad radius.

Figure 3
Figure 3 Template showing the backing plate through holes (red) and the measurement positions 1 through 7 for sample HP-1.

Figure 4 shows the measured V33 and V32 ultrasonic velocities on all seven positions of six HP-1 pads.  In this case the six pads had identical construction or “form factors”. Even though the friction material formulation for this material group was similar, the under-layer and certain processing conditions differ so we have sub-divided this group into two sub-groups labeled HP-1a and HP-1b.   It is clear from Figure 4 that the properties measured for HP-1a differ from those measured for HP-1b, with HP-1b exhibiting lower average velocities for both V33 and V32.

It should be noted here that even though the velocities have been measured by transmitting the ultrasound through the steel backing, the influence of the steel backing is removed from the data.  The values presented in Figure 4 (and throughout this paper) depend only on the friction material/under-layer properties.  The correction factor for the steel backing is on the order of 20%.  This may impart some systematic bias into the velocity data, but will not seriously impact the variability of the data.  Relative to the friction material, the steel is uniform in both thickness and elastic properties.

The Figure 4 plots are intended to show both the pad-to-pad variations and the variation within each pad.  Each plotted data point is the average value obtained from the 7 measurements on each pad. The error bar represents the standard deviation of the seven measurements. The variation in the former represents the pad to pad variations and the error bars on each point represent the variation in each pad.

Figure 4
Figure 4 V33 and V32 measurement on 6 pads comprising material group HP-1

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