Methodology

    A fourth-order Runge-Kutta scheme for solving the analytical solution of the stress field for different values of the hardening exponent n. Shooting method and an iteration scheme were used to determine the solution of the non-linear eigenvalue problem and the subsequent distributions for the stresses and displacements. The asymptotic analytical solutions were compared by finite element analysis using  highly-focused, refined meshes for the interfacial cracks and free-edge joint.

    The numerical elasto-plastic analysis allow to model the real behavior of metal-ceramic composite, when the metal components behaves elasto-plastic. The results of the elasto-plastic analysis will fully characterize plastic-zone by: dimensions r_p, interfacial load-phase angle z_p, composition of the elasto-plastic field (centered fans, constant state, elastic regions.  Different types of elasto-plastic materials were considered elastic perfectly-plastic, and Ramberg-Osgood materials with different hardening coefficients.

    Finite Element Analysis and experimental investigations of sub-interface crack propagation.

    Analytical, numerical and experimental investigations of the interaction of parallel cracks in orthotropic materials. The use of the Digital Image Correlation for tracking the crack propagation path represents a novel application of this technique, and has the advantage of full field and non contact measurement, so the experimental investigations do not influence the stress field and the crack propagation path.

Main results

    A new Four Point Bend bi-material specimen with sub-interface crack was designed.

    A methodology to determine the elastic asymptotic stress field for bi-material joints, bi-material interface cracks and cracks near interfaces was proposed based on complex variable functions.

    For elato-plastic material behaviour, like Ramberg-Osgood or elastic-perfectly-plastic, the asymptotic stress field was obtained combining Runge-Kutta algorithm for solving non-linear systems in combination with shooting method. A simple engineering formula was proposed to predict the singularity order for Ramberg-Osgood material behaviour based on the stress singularity for elastic stress field for the same joint/cracked geometry and the hardening exponent.

    For modelling the damage process in two-phase Ceramic Matrix Composites (CMC) a unified multiscale approach was developed, and is valid at different scales (micro-, meso- and macro).

    New parameters were proposed and calculated for different cracked composites for expressing the reliability of these materials:

• For the Bi-Material Four Point Bend specimens the ratio between modulus of the stress intensity factors for the bi-material K_bi and homogeneous K specimens was introduced, as a fracture parameter which takes into account the material combinations, and evaluated for different material combinations, crack lengths and crack to interface positions.

• For a normal crack to interface, typical geometry of a cracked sandwich structure, a non dimensional stress intensity factor  was calculated for different material combination between (Al₂O₃) and metals, with K_I  [MPa mm^0.5] stress intensity factor at the tip of the crack, s [MPa] applied stress and a [mm] crack length.

• A non-dimensional energy release rate parameter was defined: g = G E^CMC/[p s₁² (r+c)], where G is the energy release rate obtained numerically, E^CMC is the Young modulus of the CMC, and r+c the crack length including pore diameter and used to characterize fracture in ceramic matrix composite materials, considering cracks developed from pores at the grain boundary interface.

• A non-dimensional stress intensity factor  k_i = K_{i,orthotropic}/K_i,isotropic (with i representing the fracture mode I and II) was defined as the ratio between stress intensity factors for orthotropic material and homogeneous one.  This parameter was then evaluated numerically for two cases of parallel cracks (equal and un-equal) for different angle β of orientation for orthotropic material.

    The influence of material properties, crack length and crack position for a sub-interface crack propagation path was highlighted by numerical and experimental studies.

    Damage mechanisms in notched and un-notched sandwich composite beams under static and impact bending were identified in terms of impact energy and energy absorbed to fracture.