© 2020, The Author(s).The Hashin’s strength criteria are usually employed in first ply failure and damage-onset analysis of fibre-reinforced composites. This work presents optimality conditions of local material orientations for these criteria, in terms of principal stresses and material strength parameters. Each criterion (matrix tensile/compressive, fibre tensile/compressive modes) has its conditions separately derived, analytically, based on a fixed stress field assumption. The conditions found show that orientations which coincide and do not coincide with principal stress directions may minimise local failure indices. These solutions are employed in a proposed algorithm, named HA-OCM (Hashin Optimality Criteria Method), which selectively satisfies the matrix failure modes (either tensile or compressive), iteratively and finite element-wise in composites. It is demonstrated that the HA-OCM is able to design single-layer plane structures with improved failure loads in comparison with designs following only maximum (in absolute) principal stress orientations. Results show that the material orientations have a trend to end up either aligned or at 90° with maximum in absolute principal stress directions. Global optima for compliance are, however, not guaranteed. To give an idea of gains in terms of failure loads, some HA-OCM designs show improvements of 71% and 140%, for example, in comparison with principal stress design.

© 2020 by the authors.The present work expands the application of Puck and Schurmann Inter-Fiber Fracture criterion to fiber reinforced thermoplastic 3D-printed composite materials. The effect of the ratio between the transverse compressive strength and the in-plane shear strength is discussed and a new transition point between the fracture conditions under compressive loading is proposed. The recommended values of the inclination parameters, as well as their effects on the proposed method, are also discussed. Failure envelopes are presented for different 3D-printed materials and also for traditional composite materials. The failure envelopes obtained here are compared to those provided by the original Puck and Schurmann criterion and to those provided by Gu and Chen. The differences between them are analyzed with the support of geometrical techniques and also statistical tools. It is demonstrated that the Expanded Puck and Schurmann is capable of providing more suitable failure envelopes for fiber reinforced thermoplastic 3D-printed composite materials in addition to traditional semi-brittle, brittle and intrinsically brittle composite materials.

© 2019, Emerald Publishing Limited.Purpose: This paper aims to present experimental and numerical analyses of fused filament fabrication (FFF) printed parts and show how mechanical characteristics of printed ABS-MG94 (acrylonitrile butadiene styrene) are influenced by the void volume fraction, cooling rate and residual thermal stresses. Design/methodology/approach: Printed specimens were experimentally tested to evaluate the mechanical properties for different printing speeds, and micrographs were taken. A thermo-mechanical finite element model, able to simulate the FFF process, was developed to calculate the temperature fields in time, cooling rate and residual thermal stresses. Finally, the experimental mechanical properties and the microstructure distribution could be explained by the temperature fields in time, cooling rate and residual thermal stresses. Findings: Micrographs revealed the increase of void volume fraction with the printing speed. The variations on voids were associated to the temperature fields in time: when the temperatures remained high for longer periods, less voids were generated. The Young's Modulus of the deposited filament varied according to the cooling rate: it decreased when the cooling rate increased. The influence of the residual thermal stresses and void volume fraction on the printed parts failure was also investigated: in the worst scenarios evaluated, the void volume fraction reduced the strength in 9 per cent, while the residual thermal stresses reduced it in 3.8 per cent. Originality/value: This work explains how the temperature fields can affect the void volume fraction, Young's Modulus and failure of printed parts. Experimental and numerical results are shown. The presented research can be used to choose printing parameters to achieve desired mechanical properties of FFF printed parts.

© 2019, The Brazilian Society of Mechanical Sciences and Engineering. The present work investigates the mechanical properties of continuous carbon fiber-reinforced thermoplastic by testing composite specimens which were manufactured using an innovative process based on the fused filament fabrication (FFF, analogous to FDM ® ). The adopted testing procedures and their results are presented, as well as an introduction to the manufacturing process, which is patented by Markforged Inc. The experimental mechanical properties (stiffness and strength) of the composite specimens, measured in tensile (longitudinal and transverse), compression (longitudinal) and in-plane shear are reported. The asymptotic homogenization technique is applied in order to predict the elastic mechanical properties of the carbon fiber-reinforced lamina. In contrast to recent studies, this investigation has revealed that considering Nylon as the thermoplastic matrix embedding the continuous fiber consistently underpredicts the transverse and in-plane shear elastic properties of the reinforced laminae. These results suggest that the composition of the thermoplastic resin is not exactly the same for the unreinforced and reinforced filaments. Additionally, cross-sectional micrographs of specimens are analyzed in detail and considerable insight has been gained concerning the thermoplastic resin of reinforced filaments.

© 2018, The Brazilian Society of Mechanical Sciences and Engineering.The objective of this work is to use an asymptotic homogenization numerical model to obtain elastic properties of unidirectional fiber-reinforced composites. Square and perfect hexagonal unit cells are employed, and the influence of the fiber volume fraction over the homogenized elastic properties is studied. The effectiveness of the predictions is assessed by comparisons to experimental properties, and also another micromechanical model based on a representative volume element. The composites E-Glass 21xK43 Gevetex (glass fiber)/LY556/HT907/DY063 (epoxy matrix) and AS4 (carbon fiber)/3501-6 (epoxy matrix) were studied and good agreement between experimental and numerical predictions was found. Discrepancies between experimental and numerical data are explained in terms of simplifications considered in the homogenization model. An adjustment of properties here performed, based on varying fiber volume fractions, showed to be effective to physically represent the studied fiber composites in a micromechanical stress model based on asymptotic homogenization, developed to estimate failure envelopes of such materials.

© 2017 Elsevier LtdThe objective of this work is the mechanical characterization of materials produced by 3D printing based on fused filament fabrication (FFF, analogous to FDM®). The materials chosen are a polylactic acid (PLA) and a PLA reinforced with short carbon fibers in a weight fraction of 15% (PLA+CF). In view of the FFF nature, which produces specimens layer by layer and following predefined orientations, the main assumption considered is that the materials behave like laminates formed by orthotropic layers. If the 3D printing is made in the 1−2 plane, where 1 is the deposition direction and 2 is a direction perpendicular to 1, the mechanical properties obtained are the tensile moduli E1 and E2, the Poisson ratios ν12 and ν21, the shear modulus G12 and related strength properties. For this purpose, only unidirectional or specially oriented specimens are used. After tests up to material failure, scanning electron microscopy (SEM) is employed to observe fracture surfaces. It was noticed that, in the microstructure of the PLA+CF, the short carbon fibers stay highly oriented with the material deposition direction in the FFF specimens. This fact, and the also observed length of the fibers, explains differences in material properties encountered among the performed experiments.

© 2016 Elsevier LtdThis work focuses on the determination of failure envelopes of unidirectional fiber reinforced composites. A two scale analysis is considered and the mathematical theory of asymptotic homogenization is applied to model the problem. For a given stress applied to the macro level, it is possible to assess stresses at the micro level domain. Three regions of the micro level are considered: matrix, fiber and the interface between them, and each region is ruled by its own failure criterion. A methodology to determine failure of composites using the homogenization is proposed. In the methodology, the strengths of the composite are used to determine the strengths of the constituents: a curve fitting adjustment is applied to calculate the strengths of the matrix and an analytical procedure is used to obtain the strengths of the fiber and interface. Then, the strengths of the constituents are used to evaluate failure criteria at the micro level, and the numerical failure envelopes are built. The advantage of the proposed methodology is that it is capable of calculating numerical failure envelopes with good approximation to experimental envelopes and also to the Puck & Schürmann criterion, requiring only five unidirectional strengths of the composite as inputs.

This work presents a successful methodology for obtaining failure envelopes of unidirectional fiber reinforced composites based on micromechanical analysis by the asymptotic homogenization [1] method. Given a structure (in this case a composite material lamina) and external loads, plus having its material heterogeneity geometrically represented by a periodic unit cell of microstructure, the asymptotic homogenization method is able to predict its micromechanical stresses. Such stresses may be evaluated by failure criteria of the composite's constituents for several loading conditions, and this way it is possible to assess the composite's failure envelope. In the methodology developed, a periodic unit cell of the composite microstructure is isolated, consisting of a parallelepiped of polymeric matrix reinforced by cilindrical fibers oriented in one direction, and its behaviour is evaluated by an appropriate finite elements model. At first, the unit cell is tested in several directions to find strengths for the matrix and fiber and also matrix/fiber interface, thus evaluating failure characteristics of the composite constituents. The tests are carried out considering several possible orientations for the unit cell inside the related macroscopic media, which take into account the possible relative positions of the chosen unit cell inside the material heterogeneity of the composite. Then, the strengths of the constituents are used to predict the failure envelope for the fiber reinforced material, according to failure criteria devoted to the constituents. In this prediction, it is possible to say which is the constituent that fails first for each of the test loads. The results obtained are in good agreement with experimental data for carbon/epoxi and glass/epoxi composites. Moreover, the envelopes obtained are similar to the Puck & Schürmann [2] criterion, widely used to predict failure of such composites. This way, the present methodology renders good failure envelopes for fiber reinforced composites and gives information on the strengths of the constituents and material phase of failure, benefits from an incorporated micromechanical analysis.

© 2015, Springer-Verlag Berlin Heidelberg.The DMO (discrete material optimization) technique is employed in structural synthesis dealing with the selection of a material belonging to a group of candidate materials. It has mainly been employed in the optimization for orientation of layers of composite laminates. The DMO is based on an interpolation in the form of a weighted sum of candidate materials. The weights are nonlinear functions of penalized design variables that are solved by continuous optimization, leading to proper material selection. The preferred way of solution has been by sequential approximate optimization (SAO), based on Taylor series approximations (TSA) as surrogate functions of the structural responses. However, due to the complexity of the DMO formulation the classical local surrogate techniques become of questionable efficiency in adequately capturing structural response behavior. To improve the quality of the surrogate models, it is here proposed the use of the weighting functions to form intermediate design variables in terms of which a higher quality TSA is created. Improvements in the convergence characteristics of the SAO is observed, opening new perspectives to the efficient application of the DMO concept.

© 2015 Taylor & Francis Group, London.This paper has the aim of designing laminated composite structures to maximize vibration frequencies using concepts of hierarchical topology optimization, a structural optimization branchwhose purpose is to simultaneously design the material distribution layout of a structure in two distinct levels: One macromechanical (or structural, global) and the other micro-mechanical (or material, local). In the macro-level, design in terms of optimal material distribution on the general layout of the structure is taken into account. In the microlevel, the constitutive properties optimal design is searched, in terms of defining the distribution of material phases in unit cells of microstructure. This general approach is here extended to the laminated composites of interest: At the macro-level, optimal orientations and fiber volume fractions are defined for unidirectional composite material layers and, at the micro-level, it is designed the shape of the reinforcement fibers. The objective is to maximize the first and second natural vibration frequencies of laminated plates subjected to constraints on the limit of total fiber volume fraction employed. In this problem multiple eigenvalues are possible, leading to non-differentiability.

The aim of this work is to perform hierarchical optimization in laminated composite structures, considering simultaneously macroscopic and microscopic levels in the design of structure and material. The macroscopic level takes into account orientations and fiber volume fractions of unidirectional composite layers. The microscopic level considers the cross-sectional size and shape of the reinforcement fibers, assuming them elliptical. Both levels are coupled by a resource constraint and exchange derivatives in a mathematically consistent manner.The objective is to minimize compliance under a total fiber volume fraction constraint. The variation of the fibers' size and shape is considered by response surfaces for constitutive parameters of a reinforced lamina. Such surfaces are built from data evaluated by asymptotic homogenization techniques. The plies orientations are chosen using the Discrete Material Optimization (DMO) approach.Results in laminated plates show the influence of the reinforcement fibers' shape and volume fraction in their global behavior. The optimal microstructures obtained vary with the loading conditions considered. It is shown that the present optimization procedure permits to increase structural stiffness when material microstructural characteristics are considered. Moreover, an assessment of layers' microstructural stresses is carried out in order to evaluate the fibers' shape influence on stress concentrations. © 2013 Elsevier Ltd.

The aim of this paper is to explore the structural optimization using CATIA's built in capabilities of finite element analysis and optimization. Initially, the environment available for the integrated design, structural analysis and general optimization is discussed. Then, the characteristics of the general optimization algorithms that conduct the structural optimization are briefly reviewed. Thereafter, three problems are stated and solved, with a critical and detailed appreciation of the results obtained. Also, some simple ideas are proposed and tested to improve doing structural optimization with CATIA1. Copyright © 2008 SAE International.