Quantification of Error Associated with Using Misaligned Meshes in Continuum Damage Mechanics Material Models for Matrix Crack Growth Predictions in Composites 2385

Abstract

The ability of a material model to capture in-plane matrix mode I and mode II crack growth is an essential component for modeling ply level damage evolution in composite structures. Previous studies using a continuum damage mechanics (CDM) approach have shown success in satisfying benchmark solutions for mode I and II crack growth. However, success was shown using a fiber-aligned meshing strategy, which encourages matrix cracks to propagate in a single band of elements, along the fiber direction. Generating a fiber-aligned mesh becomes a highly involved process for laminates including off-axis (non 0° or 90°) plies. The objective of this study is to quantify the effect of non-fiber aligned mesh discretization on predictions of inplane matrix crack propagation. The approach taken incrementally varies the mesh orientation angle relative to the fiber orientation; more specifically, misaligned meshes are used to quantify the effect of element angle orientation relative to the initial crack orientation on the energy released during matrix crack propagation simulations using a CDM method. CDM solutions obtained with the misaligned meshes are evaluated against known benchmarks for mode I and II matrix crack growth. The CDM solutions reveal a near-polynomial trend of increased predicted failure stress with increased mesh misalignment angle; hence implying a potential relationship between element orientation angle and apparent fracture toughness.

Effects of characteristic element length on fracture energy dissipation in continuum damage mechanics models

“…Equation ( 13) is independent of element aspect ratio a and skew c, but does depend on the mesh misalignment w. The surface normal for the matrix crack is independent of w and always parallel to m. For a fiber-aligned mesh, equation (13) simplifies to the fiber edge length jjẽ f jj. Matrix cracks in misaligned meshes tend to grow along the mesh lines for values of w < 15 , 10 which violates the assumption that the cracking direction is parallel to f. The growth of a matrix crack along mesh lines is a consequence of the failure initiation criterion ahead of the already cracked elements being maximum within the current row of elements. A matrix crack propagating along misaligned mesh lines does not necessarily introduce error into an analysis in terms of fracture energy dissipation, as CDM material models should be designed to properly dissipate fracture energy on a per element basis.…”

“…A center notch tension (CNT) specimen comprising unidirectional fiber-reinforced material was selected for this study, based on the analyses described in literature. [3][4][5]10 The CNT problem configuration contains a central fiber-aligned matrix crack in a flat plate sized so that the crack tip stresses are unaffected by the boundary conditions. A closed-form LEFM solution is presented by Mabson et al 3 for the far-field stress r 1;c at which crack growth should occur in an infinite orthotropic plate with a center notch when loaded in tension:…”

“…Seeking a better understanding of the consequences of simplifying the mesh generation process for PDA FE models, Justusson et al 10 performed a parametric study to quantify the error associated with not aligning orthogonal meshes with the material directions, i.e., "misaligned" meshes. The authors observed that the fracture energy dissipated by matrix cracks propagating through orthogonal, misaligned meshes varied as a continuous function of the mesh misalignment angle.…”

On the importance of finite element mesh alignment along the fibre direction for modelling damage in fibre-reinforced polymer composite laminates

“…The question is posed as to whether there are modelling advantages in aligning the element and material coordinate systems, Figure 1, where, in essence, the elements align with the material fibre direction on a ply-by-ply basis. Fibre aligned mesh generation can be challenging for fibre angles beyond 0° or 90° [12] and can result in a less well-structured mesh without the use of involved seeding and biasing or partitioning of each ply. Moreover, the means of constructing a finite element mesh through the thickness may also influence the quality of the results.…”

“…To the authors' knowledge, only limited research has systematically compared results obtained from fibre aligned meshing related to those from standard meshing. For example, the angle of misalignment Centre Notch Tension (CNT) specimens, for Mode I cracking, and Centre Notch Shear (CNS) specimens, for Mode II cracking has been studied [12] while standard and fibre-aligned meshing strategies have been compared for open-hole tension (OHT) simulations [6]. This work will seek to compare results for standard and fibre-aligned meshes for different loading applications.…”