Pseudo-grain discretization and full Mori Tanaka formulation for random heterogeneous media: Predictive abilities for stresses in individual inclusions and the matrix

Abstract

For modelling damage in short fibre composites, both the predictions of the effective properties and the stresses in the individual inclusions and in the matrix are necessary. Mean field theorems are usually used to calculate the effective properties of composite materials, most common among them is Mori-Tanaka formulation. Owing to occasional mathematical and physical admissibility problems with the Mori-Tanaka formulation; a pseudo-grain discretized Mori-Tanaka formulation (PGMT) was proposed in literature. This paper looks at the predictive capabilities for stresses in individual inclusions and matrix as well as the average stresses in inclusion phase for full Mori-Tanaka formulation and PGMT for 2D-orientation of inclusions.The average stresses inside inclusions and the matrix are compared to solutions of full-scale FE models for a wide range of configurations. It was seen that the Mori-Tanaka formulation gave excellent predictions of average stresses in individual inclusions, even when the basic assumptions of Mori-Tanaka were reported to be too simplistic, while the predictions of PGMT were off significantly in all the cases. However, the predictions of the matrix stresses by the two methods were found to be very similar to each other. The average value of stress averaged over the entire inclusion phase was also very close to each other. Mori-Tanaka must be used as the first choice homogenization scheme.

A feasibility study of the Master SN curve approach for short fiber reinforced composites

“…Each fiber is represented by an ellipsoidal inclusion with its own aspect ratio, orientation and volume. We have demonstrated that this algorithm correctly calculates the homogenized elastic properties of the composite and that the stresses in fibers [31] and on the fiber-matrix interface [32] are calculated with an acceptable accuracy. We also have proven that for typical random fiber composites the degree of asymmetry of the stiffness tensor predicted with Mori-Tanaka method is limited and simple symmetrisation of the stiffness tensor provides an acceptable correction [33].…”

Effective anisotropic stiffness of inclusions with debonded interface for Eshelby-based models

“…The Mori-Tanaka (MT) formulation [3] is probably the most commonly used mean field homogenization scheme. It is known to predict with reasonable accuracy not only the effective response of the composite but also the stresses in individual inclusions [4] in spite of formal mathematical inconsistencies appearing in some specific cases [5].…”

A statistical treatment of the loss of stiffness during cyclic loading for short fiber reinforced injection molded composites

“…Using a combination of the Mori-Tanaka formulation [16] and an algorithm for treating fiber matrix debonding [17], this method predicts the local SN curve with only one SN curve as input. The approach was named the Master SN curve approach, in short the MSNC approach.…”