Mechanical Characterization and Modeling of Heterogeneous Friction Pad Material under Multiaxial Loading


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The growing need of railway transportation leads to an increase of traffic with heavier trains. Thus, in recent years, a constant improvement has been proposed on the braking system and more particularly on the friction material used. The latter is poorly known and constitutes an undeniable lever of performance improvement. The main difficulty about friction materials is their heterogeneity with a high number of components and porosity. Due to the uniaxial compression process, the properties are anisotropic. Another difficulty is the loading during braking which is multi-axial (compression+shearing) with possible microstructural transformation with temperature.

Determination of mechanical properties of friction material is not easy due to the anisotropy and multiaxial loading range conditions. Such characterization has been studied in various works with uniaxial static compression tests [1], dynamic characterization [2], ultrasonic measurements [3], etc. However such device have two types of limitation: first they are uniaxial and secondly they generally cannot be associated with a microstructural analysis to identify the associated mechanisms of deformation at the component scale (except in [1]).

In this work we propose to use another type of measurement to determine the mechanical properties of friction material, with a multiaxial test combined with numerical models and microanalysis:

  • Determining anisotropic properties with a single multiaxial test (indentation) combined with an original numerical method of mechanical properties identification
  • Identifying the microstructural mechanisms associated to these properties, by doing indentation test in a microtomograph, and also combined with an heterogeneous modeling

The proposed methodology is as follows:

  • Work with reduced formulations for the physical comprehension, because the friction materials are particularly complex.
  • Extend these approaches by adding multiaxial solicitation. Thus, the method used consists of highly instrumented indentation tests ([4], [5] and [6]), and indentation tests under X-ray microtomograph ([7]).
  • Reproduce numerically these tests using the finite element method [8], to better understand and quantify the mechanisms involved. In these numerical tests, an original approach is proposed by decomposing the material law (decomposition in Kelvin mode ([9], [10])), thus decoupling the complexity of the problem. This rewriting makes it possible, through reverse identification [11], to obtain quantitative information on the material law.
  • Complete the experimental base and reinforce the identification of the model with additionally tests (ultrasonic tests [3], etc).

The major results are :

  • The identification of anisotropic mechanical properties with a minimum of tests using the decomposition in Kelvin mode
  • Identification of the properties under the multiaxial solicitations and link them with microstructural evolutions of the material

This original mechanical properties identification has been applied to friction materials for railway application. Comparisons have been done with uniaxial compression tests and with ultrasonic measurements. Results show the interest of such test and highlight some micromechanisms leading to these properties.


[1] R. MANN, Relation between mechanical behavior and microstructure of a sintered material for brake applications, Wear, Volumes 386–387, 15 September 2017, Pages 1-16

[2] Hornig, S. and Von Wagner, U. Experimental identification of brake lining material properties subjected to combined static and High Frequency Loading - A Step Towards a Better Prediction of Disc Brake Squeal, SAE Technical Paper 2011-01-2353, 2011

[3] Industrial Measurement Systems. IMS

[4] S. KOSSMAN, Indentation instrumentée multi-échelles de matériaux homogènes et multi-matériaux, 2017 Matériaux & Techniques Volume 105, Number 1, 2017

[5] I.N. SNEDDON, The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile, International Journal of Engineering Science, pages 0047-0057, 1965.

[6] D. TABOR, A Simple Theory of Static and Dynamic Hardness, Proc. R. Soc. Math. Phys. Eng. Sci , pages 0247-0274, 1948.

[7] ISIS 4D (In Situ Innovative Set-ups under X-ray microtomography)

[8] ABAQUS 6.14, Dassault

[9] R. DESMORAT, Non-quadratic Kelvin modes-based plasticity criteria for anisotropic materials, International Journal of Plasticity, 2011

[10] A. BONA, Coordinate-free Characterization of the Symmetry Classes of Elasticity Tensors, J Elasticity, 2007.

[11] MARQUARDT D. (1963) An Algorithm for Least-Squares Estimation of Nonlinear Parameters, SIAM J. Appl. Math.11 431-441

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