Search

• An initial yield surface is established and proposed for cellular materials. • Five loading cases are considered to evaluate the performance of the yield surface. • Five sheet-based triply periodic minimal surface lattices are investigated. • The proposed yield criterion shows accurate yielding predictions for all cases. Triply periodic minimal surfaces (TPMS), which are a class of architected cellular materials, have attracted significant attention lately, due to their prevailing mechanical, electrical and chemical properties, to name a few, and due to the advancements in additive manufacturing technologies that make it possible to print such materials. However, simulating the elastic-plastic mechanical behavior of structural systems (e.g., beams, plates, cores of sandwich panels, structural systems with various levels of geometric complexity) that are latticed with thousands of TPMS lattices are computationally expensive to model explicitly, and hence the need to develop accurate yield surfaces in order to capture their plastic behavior in a homogenized approach. In this work, a generalized initial yield criterion is proposed for sheet-based TPMS lattices, which incorporates the Lode parameter L. The initial yielding of five different sheet-based TPMS lattices are investigated in five different loading conditions. These lattices are Schoen's I-WP (IWP-s), Gyroid (GYR-s), Diamond (DIA-s), F-RD (FRD-s) and Primitive (PRIM-s). The proposed yield criterion accurately predicts the initial yielding of all these lattices in all the loading conditions considered, outperforming other yield criteria currently proposed in literature. [Display omitted] [ABSTRACT FROM AUTHOR]

Owing to the advancements in additive manufacturing and increased applications of additively manufactured structures, it is essential to fully understand both the elastic and plastic behavior of cellular materials, which include the mathematically-driven sheet lattices based on triply periodic minimal surface (TPMS) that have received significant attention recently. The compressive elastic and plastic behaviors have been well established for many TPMS latticed structures, but not under multiaxial loading. Furthermore, TPMS lattices are computationally expensive to model explicitly when used in latticing various structures for enhanced multi-functionality, and hence the need to develop accurate yield surfaces in order to capture their plastic behavior in a homogenized approach. The majority of previous yield surfaces developed for cellular materials originate from cellular foams, and limited attempts has been made to develop yield surfaces for TPMS lattices. In this study, a numerical modeling framework is proposed for developing the initial yield surface for cellular materials and is used to develop the initial yield surface for Schoen's IWP sheet-based TPMS cellular lattices. The effect of different loading conditions on the effective yield strength of the IWP sheet-based (IWP-s) TPMS lattice is numerically investigated, based on a single unit cell of IWP-s under fully periodic boundary conditions, assuming an elastic-perfectly plastic behavior of the base material, for relative densities (ρ ‾) ranging from 7% to 28%. In order to account for different loading conditions, the stress state is characterized in a generalized fashion through the Lode parameter (L). The effect of L is studied over a range of mean stress values (σ m) to understand the effect of both L and σ m on the effective yield strength. An initial yield surface is developed incorporating the effect of L , σ m and ρ ‾ , and is validated numerically showing rather good agreement. In the 3D principal stress space, the shape of the yield surface for the IWP-s lattice resembles the shape of a cocoa pod. [Display omitted] • Extensive numerical finite element simulations on Schoen's IWP triply periodic minimal surface. • An initial yield surface is established and proposed for cellular materials, accounting the third deviatoric stress invariant J 3 , through the incorporation of Lode parameter L. • The initial yield surface is validated at three different loading cases, and is compared to other three well established yield surface for cellular materials. • Proposed yield surface has predicts the initial yielding of IWP-TPMS markedly well. [ABSTRACT FROM AUTHOR]

Abstract: Experiments on double notched tube specimens subjected to tension and torsion were conducted by Barsoum and Faleskog (2007) [8,9]. In this study a complementary experimental investigation was conducted on tensile round circumferentially notched bar specimens. The results from the current study were compared with the results from the double circumferentially notched tube specimens with stress triaxiality larger than 0.7 in order to asses the influence of the Lode parameter on ductility in the moderate stress triaxiality regime. The effective plastic strain, the stress triaxiality T and the Lode parameter L were determined at the center of the notch up to the point of onset of failure by means of finite element. The influence of the Lode parameter on the failure strain was significant for the high strength and low hardening material, whereas for the medium strength and high hardening material the influence of the Lode parameter was less distinguished. The experimental results were then analyzed with the micromechanical model proposed by Barsoum and Faleskog (2011) [15], which is based on the assumption that ductile failure is a consequence of that plastic deformation localizes into a band. The band consists of a square array of equally sized cells, with a spherical void located in the center of each cell, which allows for studying a single 3D unit cell with fully periodic boundary conditions. The unit cell is subjected to a proportional loading such that it resembles the stress state, in terms of T and L, from the experiments. The micromechanical model captures the experimental trend and the influence of L on ductility very well. It is found that the Lode parameter sensitivity increases by the combination of increase in the yield strength and decrease in strain hardening. The fractographical analysis reveals that this Lode parameter sensitivity is associated with the failure characteristics of the material. [Copyright &y& Elsevier]

Abstract: A micromechanical model consisting of a band with a square array of equally sized cells, with a spherical void located in each cell, is developed. The band is allowed a certain inclination and the periodic arrangement of the cells allow the study of a single unit cell for which fully periodic boundary conditions are applied. The model is based on the theoretical framework of plastic localization and is in essence the micromechanical model by Barsoum and Faleskog (Barsoum, I., Faleskog, J., 2007. Rupture mechanisms in combined tension and shear—micromechanics. International Journal of Solids and Structures 44(17), 5481–5498) with the extension accounting for the band orientation. The effect of band inclination is significant on the strain to localization and cannot be disregarded. The macroscopic stress state is characterized by the stress triaxiality and the Lode parameter. The model is used to investigate the influence of the stress state on void growth and coalescence. It is found that the Lode parameter exerts a strong influence on the void shape evolution and void growth rate as well as the localized deformation behavior. At high stress triaxiality level the influence of the Lode parameter is not as marked and the overall ductility is set by the stress triaxiality. For a dominating shear stress state localization into a band cannot be regarded as a void coalescence criterion predicting material failure. A coalescence criterion operative at dominating shear stress state is needed. [Copyright &y& Elsevier]

Abstract: A micromechanics model based on the theoretical framework of plastic localization into a band introduced by Rice is developed. The model consists of a planar band with a square array of equally sized cells, with a spherical void located in the centre of each cell. The periodic arrangement of the cells allows the study of a single unit cell for which fully periodic boundary conditions are applied. The micromechanics model is applied to analyze failure by ductile rupture in experiments on double notched tube specimens subjected to combined tension and torsion carried out by the present authors. The stress state is characterized in terms of the stress triaxiality and the Lode parameter. Two rupture mechanisms can be identified, void coalescence by internal necking at high triaxiality and void coalescence by internal shearing at low triaxiality. For the internal necking mechanism, failure is assumed to occur when the deformation localizes into a planar band and is closely associated with extensive void growth until impingement of voids. For the internal shearing mechanism, a simple criterion based on the attainment of a critical value of shear deformation is utilized. The two failure criteria capture the transition between the two rupture mechanisms successfully and are in good agreement with the experimental result. [Copyright &y& Elsevier]