Fracture Toughness Determination on an SCB Specimen by Meshless Methods

Farid Mehri Sofiani,Behzad V Farahani,Jorge Belinha

doi:10.3390/app12052633

Abstract

This work investigates fracture characteristics of a marble semi-circular bend (SCB) specimen with a pre-defined crack under a compressive loading condition. It aims at evaluating how the fracture toughness can be affected by the crack and span length variation. Numerically, the model is solved using meshless methods, extended to the linear elastic fracture mechanics (LEFM), resorting to radial point interpolation method (RPIM) and its natural neighbor versions (NNRPIMv1 and NNRPIMv2). Alternatively, to validate the meshless method results, the problem is resolved following the finite element method (FEM) model based on the standard 2D constant strain triangle elements. As a result, fracture toughness and the critical strain energy release rate are characterized following the testing method on the cracked straight through semi-circular bend specimen (CSTSCB). A comparison is drawn amongst the theoretical, meshless methods and FEM results to evaluate the capability of advanced numerical methods. Encouraging results have been accomplished leading to validate the supporting numerical methodologies.

Highlights

In relation to the nodal connectivity in neighbor radial point interpolation method (NNRPIM), it is made by a set of nodes in the neighborhood of an interest point xi ∈ X, the NNRPIM influence-cell notion contributes to forming the node connectivity
Different crack lengths and spans were taken into account led to obtaining the numerical results using meshless method formulations, see Table 2
The numerical model was prepared through the finite element method (FEM) in FEMAP© software and the essential data of Finite Element (FE) mesh was exported to feed the numerical algorithms developed in MATLAB©

Summary

Introduction

The capability to endure a substantial amount of damage is a demand for current engineering structures; it has become progressively imperative to improve methodologies to anticipate failure phenomenon in damaged components. The critical strain energy release rate describes the resistance of the material against the crack growth In this regard, Almeida-Fernandes et al [5] developed numerical damage models calibrated with experimentally based fracture toughness parameters on the pultruded glass fiber reinforced polymers. Meshless methods have never been employed to calculate fracture toughness and critical strain energy release rate for SCB specimens. Despite FEM, meshless methods do not require FE remeshing which is undesirable in terms of crack propagation problems and solution convergences on the nonlinearity in the engineering structures with complex material behaviors such as damage mechanics or porous models, c.f. The main contribution of this work can be related to the development of meshless method formulations combined with LEFM theory It contributed to elastostatically simulating the cracked domain in order to attain the fracture toughness and critical strain energy release rate

Overview on Meshless Methods

Mathematical Formulation

Analysis, Results and Discussion

Conclusions