Stéphane Baste

Development of damage in a 2D woven C/SiC composite under mechanical loading: I. Mechanical characterization

Abstract An investigation has been undertaken to determine the damage mechanisms and the associated mechanical response of a 2D reinforced composite of carbon fibers in an SiC CVI-processed matrix subjected to uniaxial tensile and compressive loadings at room temperature. Under tension loading, an extended non-linear stress/strain response was evidenced and related to a multi-stage development of damage involving transverse matrix microcracking, bundle/matrix and inter-bundle debonding as well as thermal residual stress release. This tensile behavior proved to be damageable-elastic with respect to a fictitious thermalstress-free origin of the stress/strain axis lying in the compression domain. In compression, after an initial stage involving closure of the thermal microcracks present from processing, the composite displayed a linear-elastic behavior until failure. The extent of damage over the material was characterized quantitatively at the microscale by the decrease of the average transverse microcrack spacing and at the macroscale by the decrease of both the longitudinal Youngs modulus and the in-plane Poissons ratio.

Optimal determination of the elastic constants of composite materials from ultrasonic wave‐speed measurements

A method is described to optimally determine the elastic constants of anisotropic solids from wave‐speeds measurements in arbitrary nonprincipal planes. For such a problem, the characteristic equation is a degree‐three polynomial which generally does not factorize. By developing and rearranging this polynomial, a nonlinear system of equations is obtained. The elastic constants are then recovered by minimizing a functional derived from this overdetermined system of equations. Calculations of the functional are given for two specific cases, i.e., the orthorhombic and the hexagonal symmetries. Some numerical results showing the efficiency of the algorithm are presented. A numerical method is also described for the recovery of the orientation of the principal acoustical axes. This problem is solved through a double‐iterative numerical scheme. Numerical as well as experimental results are presented for a unidirectional composite material.

Optimal recovery of the elasticity tensor of general anisotropic materials from ultrasonic velocity data

An ultrasonic wave approach is presented for the optimal identification of the 21 independent elasticity constants of the most general linear homogeneous anisotropic elastic solid from wave speed measurements of obliquely incident ultrasonic bulk waves. Since the symmetry of acquisition planes is not taken into account, this inversion process is generalized to materials that do not possess three mutually orthogonal planes of symmetry. Minimization of an overdetermined system of nonlinear algebraic equations is solved by a constrained optimization method. Various classes of symmetry are considered. Several critical factors (initial guesses, scatter in experimental data) which can influence the accuracy of the elastic property reconstruction algorithm have been investigated by means of numerical examples that simulate in the best way a typical experiment. The sensitivity of the reconstruction algorithm to each identified elasticity constant is detected a posteriori by means of the estimation of a confidence...

Effect of microcracking on the macroscopic behaviour of ceramic matrix composites: Ultrasonic evaluation of anisotropic damage

Abstract This paper studies the effect of matrix microcracking within a SiC-SiC composite on its macroscopic behaviour. Experimentally, ultrasonic evaluation under load is used. Ultrasonic velocities are measured for varying propagation directions as a function of applied stress. The anisotropic stiffness degradation due to the applied stress is determined from ultrasonic velocity measurements. This anisotropic stiffness degradation is a function of microcrack evolution and accumulation in the damaged composite. The theoretical approach is developed in the framework of continuum damage mechanics. Two internal variables are introduced to distinguish between microcrack initiation, distribution and growth on one hand, and microcrack evolution with applied stress, closing or opening without growth on the other hand. This model taking into account the initial state of the material is well adapted to the behaviour of this SiC-SiC composite for which matrix microcracking is the fundamental mechanism of degradation. Coupled with ultrasonic evaluation, this model allows to assess completely the accumulated damage in the investigated principal plane and in particular to find the loading history of the material.

Inelastic behaviour of ceramic-matrix composites

Abstract A methodology for the formulation and identification of the constitutive laws of ceramic-matrix composites is summarised. It relies on an anisotropic damage evaluation that accurately separates the effects of the various damage mechanisms on the non-linear behaviour. A mixed approach takes into account the basic strain and damage mechanisms by using a homogenisation method that provides the relationship between the mechanical response and the intensity of damage in the individual modes. That leads to a non-arbitrary choice of internal variables in the macroscopic constitutive relationships. A successive process of prediction/experimental-data confrontation allows the optimal determination of the evolution laws of those internal variables. This methodology is illustrated on various behaviours of various CMCs; several crack arrays, tilted cracks, tensile test, cyclic loading, off-axis solicitation, in 1D SiC–SiC, 2D C–SiC, 2D C/C–SiC ceramic-matrix composites. Predictions of the three-dimensional changes in elasticity and of the inelastic strains are shown to compare favourably with experimental data measured with an ultrasonic method.

Induced anisotropy and crack systems orientations of a ceramic matrix composite under off-principal axis loading

The effect of matrix microcracking on a ceramic matrix composite (CMC) is studied by means of an ultrasonic method. It provides the whole set of the stiffnesses of materials that possess any class of symmetry (including the most general anisotropy), and then the simultaneous identification of the angular parallax locating the higher symmetry coordinate system and the associated optimal stiffness tensor. The problem of damage-induced anisotropy, i.e., the orientation of the matrix microcracks comparative to the loading direction and to the material axes of the composite, may be treated without the limiting assumption that the material keeps its orthorhombic symmetry in an a priori known coordinate system. The induced anisotropy depends on the loading direction. If a tensile solicitation in one of the fiber directions induces damage modes that are parallel to one of the elasticity principal planes, a tensile solicitation along a non-principal direction creates microcracks with a predominant orientation that does not coincide with the elastic symmetry axes, and induces a fully anisotropic elastic degradation. The load-induced rotation of the elasticity principal coordinate system is emphasized. Finally, the assessment of the crack orientation, from the wave speed measurements, points out that the loading direction and the fiber directions both govern the direction of the crack growth.

Identification of complex stiffness tensor from waveform reconstruction.

An inverse method is proposed in order to determine the viscoelastic properties of composite-material plates from the plane-wave transmitted acoustic field. Analytical formulations of both the plate transmission coefficient and its first and second derivatives are established, and included in a two-step inversion scheme. Two objective functions to be minimized are then designed by considering the well-known maximum-likelihood principle and by using an analytic signal formulation. Through these innovative objective functions, the robustness of the inversion process against high level of noise in waveforms is improved and the method can be applied to a very thin specimen. The suitability of the inversion process for viscoelastic property identification is demonstrated using simulated data for composite materials with different anisotropy and damping degrees. A study of the effect of the rheologic model choice on the elastic property identification emphasizes the relevance of using a phenomenological description considering viscosity. Experimental characterizations show then the good reliability of the proposed approach. Difficulties arise experimentally for particular anisotropic media.

Optimal determination of the material symmetry axes and associated elasticity tensor from ultrasonic velocity data

A simultaneous identification of the angular parallax locating the higher symmetry coordinate system and the associated optimal stiffness tensor from wave speed measurements of obliquely ultrasonic bulk waves in an arbitrarily oriented coordinate system is presented. The property used in classifying a material with regard to its elastic symmetry is the existence and the number of planes of reflective or mirror symmetry. That leads to considering the problem of determining the symmetry class and the directions of the elements of symmetry. To consider the uncertainties of the experimental data, the wave speed measurements are only used to determine the symmetry frames and the optimal stiffness tensor. The proposed inverse propagation algorithm consists of minimizing a functional where the unknowns are the elasticity constants and the Euler angles between the geometric coordinate system and the frame of higher symmetry. Stability of the used least-square algorithm to the initial guesses and to the noise in t...

An Experimental Investigation of Stiffness Reduction and Cracks Geometry in a Unidirectional Brittle Matrix Composite

The nonlinear mechanical behavior of a unidirectional ceramic matrix composite is investigated by means of an ultrasonic method. This paper presents measurements of all the stiffness tensor coefficients during each step of a tensile test, and consequently the variation of all the components of the anisotropic damage tensor. A description in terms of compliance makes possible comparison between mechanical and ultrasonic measurements of the composite deterioration and the re-construction of the stress-strain curve from ultrasonic data. Good agreement between both experimental and predicted compliances of an anisotropic medium with distributed slit cracks is found. From this comparison, the crack density parameter is estimated and the matrix cracks geometry is characterized.

Cracking orientation and induced anisotropy of a ceramic matrix composite under off-axis loading

The effect of matrix microcracking on the stiffnesses of a carbon-fibre/SiC-matrix woven composite is studied by means of an ultrasonic method. It provides the whole set of the stiffness tensor coefficients which are inaccessible by classical strain measurements and which are required to identify anisotropic damage. The induced anisotropy depends on the loading direction. If a tensile solicitation in a fibre direction leads to stiffnesses decreases without any rotation of principal axes, a tensile solicitation of 45° from a fibre direction creates microcracks with a predominant orientation that does not coincide with the elastic symmetry axes, and induce a fully anisotropic elastic degradation.