Damage and Lifetime Modeling for Structure Computations

Abstract

INTRODUCTIONCeramic matrix composites (SiC fibers, PyC interphase, and mutistacked Si-B-C matrix in this paper) combine good mechanical properties with the capability of sustaining high temperatures in oxidizing environments. The use of a multilayer self-healing matrix improves the lifetime of ceramic matrix composites (CMCs) considerably [1]. This technology along with the use of SiC fibers paves the way for applications with very long lifetimes (several thousands of hours).Structural applications of CMCs need to answer to the main and critical question that is at the center of this chapter: how to predict, that is, to compute, the lifetime of engineering structures. The answer is a multiphysic macroscopic model able to reproduce couplings between the mechanical and environmental fields. For such materials, confidence in the simulation is related directly to one's understanding of each degradation mechanism and to the introduction of such mechanisms in the model; lifetimes being too large for a purely experimental validation over long lifetimes (tens of thousands of hours).The first part of the chapter deals with the modeling of the different microcracking mechanisms. The key phenomenon is the deflection of the matrix cracks in the fiber matrix interphase [2][3][4]: this mechanical fuse protects the fibers from the cracks and enables the development of multiple cracks in the matrix, giving the composite some level of ductility, even though all of its constituents are brittle. The matrix cracking scenario has already been established for woven CMCs [5]. Since the matrix between the yarns is stiffer, but more brittle, and has larger pores than the yarns themselves, it begins to crack first. For a well-densified composite, the corresponding cracks are oriented by the main loading direction and are orthogonal to the applied stress direction, which is a main modeling difficulty. Then, when this crack network nearly reaches saturation, new cracks mainly appear in the matrix inside the yarns. The corresponding cracks are oriented by the fibers: they are orthogonal to the fibers in the longitudinal yarns, and parallel to the fibers in transverse yarns if the main load direction corresponds to the longitudinal yarns. In summary, there are three types of cracks in the damaged material: (i) inter-yarn cracks, (ii) intra-yarn longitudinal cracks, and (iii) intra-yarn transverse cracks.Among composites, CMCs are the most difficult situation for damage modeling. Rather complex closure effects occur for the damage mechanism associated with microcracks when direction is orthogonal to the loading direction and, therefore, is not known a priori. Here, we are developing our answer with a general anisotropic damage theory including microcracks closure effects [6,7]. In order to differentiate between the crack opening and closing effects, which are very pronounced in CMCs, the strain energy is divided into three parts associated with damage due to pure traction, Ceramic Matrix Composites: Materials, Modeling and Technology, First Ed...

A convex anisotropic damage model based on the compliance tensor

“…The compliance tensor has been used as the primary damage variable before (Baranger, 2018;Ladev eze, 1983Ladev eze, , 2002Ladev eze et al, 2014). Yet, this approach has not yet entered the main stream of damage-modeling frameworks.…”

Accounting for frictional contact in an anisotropic damage model based on compliance tensorial variables, illustration on ceramic matrix composites

“…With the proposed positive and negative parts, the state potential is convex with respect to σ as demonstrated in Ladevèze et al. (2014).…”

Extension of a fourth-order damage theory to anisotropic history: Application to ceramic matrix compostites under a multi-axial non-proportional loading

“…This is due to the presence of terms mixing eigenvalues as shown in Ladeveze (1983). With the proposed positive and negative parts, the state potential is convex with respect to σ as demonstrated in Ladevèze et al. (2014).…”

“…Model (1) In Ladevèze (2002), the damage is driven by the stress. This model is noted (1), the evolution laws read The dissipated power ω· reads Model (2) In Ladevèze et al. (2014), the strain is privileged.…”