Damage law identification of a quasi brittle ceramic from a bending test using Digital Image Correlation

Abstract

The quasi brittle ceramics show a non linear mechanical behaviour resulting most of the time in a dissymetry between their tensile and compressive stress-strain laws. The characterization of their fracture strengths might be biased if elastic linear formulae are used to analyze classical tests like bending tests. Based on Digital Image Correlation (DIC), a methodology is proposed to characterize materials with dissymmetric behaviours. Applying specific DIC decomposition functions for bending, compressive and tensile tests, a stress-strain model and its damage law are identified for aluminium titanate, a damageable micro cracked ceramic. This identification method using DIC can obviously be applied to other quasi brittle materials.

Computational measurements of stress fields from digital images

“…The particular case of crack tip fields required the use of Williams' series as basis functions [10]. Other specific bases, like for 4-point bending test [11] or Brazilian test [12] can be used but for arbitrary displacement, finite element based [4,13] or CAD based kinematics [14,15] are more appropriate. From a first guess for the displacement, an iterative prodecure is run until convergence is reached.…”

New advances in the laboratory characterization of refractories: testing and modelling

“…In our case, for 4-point bending, the kinematic is analytically known according to the Bernoulli beam theory. Thus, a small number of global degrees of freedom is sufficient to describe the entire displacement field u(x,y) on the sample [16]:…”

Identification of damage and cracking behaviours based on energy dissipation mode analysis in a quasi-brittle material using digital image correlation

“…However, such general decompositions do not allow for a direct extraction of searched mechanical quantities (Young's modulus, Poisson's ratio, damage law, stress intensity factors…). If additional information is known concerning the form of the searched displacement, some global kinematic assumptions can be introduced through specific displacement basis functions ψ n : Roux and Hild (2006) used Williams' series around the tip of a crack for handling stress intensity factor measurements, Hild et al (2009) have employed a linear curvature element for accounting for cantilever beam kinematics, Leplay et al (2010) used specific functions for four-points bending and uniaxial tests kinematics. NURBS functions were also used by Réthoré et al for handling high order beam kinematics ).…”

“…This procedure is particularly attractive because of the direct connection between experiments and simulations, since the kinematic bases may be identical in both cases. A large variety of specific basis functions may be used to integrate a chosen displacement decomposition into the measurement problem, like for beam kinematics Leplay et al 2010;) or fracture kinematics . These approaches, called herein integrated digital image correlation (I-DIC), have been already associated with identification methods to quantify mechanical properties , establish damage laws (Leplay et al 2010) and determine stress intensity factors ).…”

“…A large variety of specific basis functions may be used to integrate a chosen displacement decomposition into the measurement problem, like for beam kinematics Leplay et al 2010;) or fracture kinematics . These approaches, called herein integrated digital image correlation (I-DIC), have been already associated with identification methods to quantify mechanical properties , establish damage laws (Leplay et al 2010) and determine stress intensity factors ). Unlike I-DIC approaches based on kinematics assumptions, it is also possible to a priori assume the mechanical behaviour of the material.…”