Equivalent Material Concept Research Articles

Tensile fracture prediction of 3D-printed V-notched PLA specimens: Application of VIMC-MEMC in conjunction with brittle fracture criteria

This study investigates the fracture behavior of additively manufactured round-tip V-notched diagonally loaded square plate (RV-DLSP) specimens with different notch opening angles and tip radii produced from the Polylactic acid (PLA) with [0/90/45/-45]s raster orientation using the fused deposition modeling (FDM) technique. PLA is known for its ductile behavior, making it a suitable material for various engineering applications. Also, the layer-wise manufacturing process in FDM technique makes the PLA specimens be actually anisotropic. To take the nonlinearity and anisotropy of PLA simultaneously into consideration in prediction of the fracture loads of RV-DLSP specimens, the present study employs the Virtual Isotropic Material Concept (VIMC) and modified Equivalent Material Concept (MEMC) in a two-level strategy of simplifying PLA to an isotropic linear elastic virtual material. Then, the mean stress (MS) and maximum tangential stress (MTS) criteria are utilized to estimate the fracture loads. The theoretical estimations reveal that the VIMC-MEMC-RV-MS criterion is the most accurate model, demonstrating its effectiveness in predicting the fracture behavior of RV-DLSP specimens. Additionally, the VIMC-MEMC-RV-MTS criterion shows commendable accuracy, particularly for the specimens with 30 (deg.) notch opening angle. The scanning electron microscopy (SEM) analysis of the fracture surfaces provides further insights into the fracture mechanisms of RV-DLSP specimens. Notably, distinct fracture patterns are observed based on variations in the notch geometry. Specimens with smaller notch tip radii exhibit fiber cleavage, while those with larger radii display greater fiber interpenetration. These SEM observations are consistent with the fracture load data, which indicates higher fracture loads with increasing the notch opening angle and tip radius. By integrating VIMC and MEMC with the two fracture criteria, accurate predictions of the notch fracture toughness can be achieved, facilitating the design and optimization of 3D-printed PLA components against fracture.

A simple, fast, and robust criterion for predicting fracture load and crack growth path in notched elastoplastic plates under mixed-mode loading

This study assesses the combined in-plane tensile/shear failure of aluminum plates containing notches. With this aim, a numerical method, i.e., the so-called equivalent material concept (EMC) in association with the extended finite element method (XFEM), is introduced to simulate the fracture phenomenon. The predicted failure load, initiation angle, and growth path are compared to experimental results reported for aluminum alloys in the literature to evaluate the functionality of the proposed method. Also, the accuracy of the EMC-XFEM model was compared to the conventional Ductile Damage method. The EMC-XFEM combined model is found to be fast and robust with appropriate accuracy in fracture predictions of ductile samples in comparison with the elastoplastic damage model and experimental data.

Experimental and theoretical investigation of the influence of post-curing on mixed mode fracture properties of 3d-printed polymer samples

This study explores the mechanical properties and fracture characteristics of additively manufactured acrylonitrile butadiene styrene specimens, focusing on the impact of raster angle and post-process heat treatment. To this end, a large number of tensile and semi-circular bending samples with three distinct raster angles of 0/90°, 22/ − 68°, and 45/ − 45° were prepared and exposed to four types of heat treatments with different temperature and pressure conditions. Simultaneously, theoretical models of maximum tangential stress (MTS) and generalized MTS (GMTS) were developed to estimate the onset of specimen fracture under mixed-mode in-plane loading conditions. Recognizing the non-linear behavior within the stress–strain curve of tensile test samples, particularly in the annealed samples, an effort was undertaken to transform the original ductile material into a virtual brittle material through the application of the equivalent material concept (EMC). This approach serves the dual purpose of bypassing intricate and tedious elastoplastic analysis, while concurrently enhancing the precision of the GMTS criterion. The experimental findings have revealed that while the annealing process has a minimal effect on the yield strength, it considerably enhances energy absorption capacity, increases fracture toughness, and reduces the anisotropy. Additionally, the combined EMC-GMTS criterion has demonstrated its capability to predict the failure of the additively manufactured parts with an acceptable level of accuracy.

Measurement of the interfacial energy release rate (ERR) and cohesive law parameters of polyvinyl butyral laminated glass using a novel beam-type test specimen

The polyvinyl butyral (PVB) laminated glass (LG) structures are widely used in architectural and automotive sectors. Determination of the interfacial fracture energy (i.e. G) between the PVB layer and glass is one of the most vital procedures for ensuring the structural safety and fracture resistance of these kinds of components. The present study investigates the adhesion characteristics between glass and PVB interface in a LG composite structure. A new simple test fixture is introduced to measure the mixed-mode fracture energy from pure mode I (i.e. GI) to pure mode II (i.e. GII). By making use of the concept of Equivalent material Concept (EMC), linear elastic fracture mechanics (LEFM) formulations together with finite element (FE) analysis can be used to compute the compliance parameter of the system and pure modes I/II fracture energies. Besides, the interaction of cohesive forces between the PVB layer and glass are simulated by using a FE method based on a bi-linear cohesive zone model (CZM) technique. In this regard, the cohesive law parameters are computed for mode I and mode II in an iterative process. Then, the obtained pure mode cohesive law parameters are utilized to predict the mixed-mode load–displacement diagrams. The obtained results demonstrate the satisfactory accuracy of the cohesive law parameters and fracture energies in predicting the mixed-mode loading results across four different loading rates (i.e. LR = 2, 5, 10, and 15 mm/min).

Effect of nozzle diameter and raster orientation on tensile and fracture behavior of FDM‐PLA specimens under mixed‐mode I/II loading

AbstractFused deposition modeling (FDM) is a material extrusion technique that works by extruding molten filament on a heated platform. In this method, several manufacturing parameters are engaged which affect the mechanical performance of printed parts. In this study, the effects of nozzle diameter on tensile (under two loading rates) and mixed‐mode I/II fracture behavior of printed specimens were examined. The obtained results revealed that testing speed had a minor effect on basic mechanical properties. For instance, ultimate tensile strengths of tensile specimens printed with 1 mm nozzle diameter were 32.56 and 39.71 MPa for test speeds of 1 and 5 mm/min, respectively. Higher nozzle diameters resulted in higher mechanical properties and fracture resistance (e.g., specimens printed with 45/−45° raster angle with 0.4 and 1 mm nozzle diameters indicated fracture loads of 4520 and 5071 N, respectively). Besides, fracture loads were predicted through the equivalent material concept coupled with J‐integral method.

Assessment of different forecasting strategies for the breaking load resistance in notched specimens 3d-printed in PLA using additive manufacturing (FFF) technology

The introduction of fused deposition modelling in the industrial sector to produce functional components in thermoplastic materials, such as PLA, requires knowledge of the performance limits of such elements during the design phase. Predicting the breaking load resistance of notched specimens is essential to evaluate the mechanical performance of components manufactured using this technology. This study compares different methodologies based on the critical distance criterion (TCD) for predicting the static breaking strength of printed notched specimens made with Fused Filament Fabrication (FFF) technology using PLA material. Specimens with different topologies of V-notches were printed according to a standardized configuration. Various analysis techniques were applied to determine the breaking strength of each specimen. By comparing the results obtained with experimental data to assess their accuracy and reliability, it has been demonstrated that these methodologies, coupled with the concept of equivalent elastic material (EMC), can be useful for predicting static breaking load.

Functionally graded thick-walled tubes analysis by numerical methods

Functionally graded materials are increasingly used in the practice of engineering design, as is the case with thick-walled tubes. The use of these constructive elements requires a calculation, which should be as accurate, as accessible and as fast as possible. The present work responds to these requirements. For the calculation of tubes with thick walls made of functionally graded materials, two new ways were used, based on the concepts of multilayer (material) wall and equivalent material. The multi-layered wall concept considers the tube wall made of several layers, as in the case of the well-known multilayer plates, and the equivalent material concept considers the thick-walled tube made of homogeneous and isotropic material, but with fictitious properties, equivalent in behavior to the functionally graded material. The influence of Poisson's ratio is illustrated by some comparative results. The development of the calculus, the validation of the models and the analysis of the results are based on the numerical calculus using the finite element method. The models used, the transverse plane model, the axial-symmetric plane model and the 3D longitudinal model, are made in several variants regarding the fineness of the mesh. The paper also analyzes the influence of the Poisson ratio variation, compared to adopting a constant value. The results of the study, the models and concepts used are useful to specialists and designers of structures of this type, they have a high degree of generality and present openings for the use of other calculation methods.

Radial Displacements in a Rotating Disc of Uniform Thickness Made of Functionally Graded Material

The finite element method is used to calculate a rotating disc, which has a uniform thickness and is made of functionally graded materials, based on the concepts of multilayer disc and equivalent material. These concepts are also available for analytical calculus. The multilayered disc concept perceives the disc as constructed from several layers, and the equivalent material concept regards the disc material as composed of homogeneous and isotropic material but with fictitious properties equivalent in behavior to the functionally graded material. These two concepts, encompassed in this study, allow us to contemplate the variation according to the material law and Poisson's ratio, which is often neglected, to reduce the mathematical complexity. The concepts, models, and methods involved in this study were validated by employing numerical and analytical calculations. The proposed method introduced simplicity, precision, and accessibility to solve the complex problem of functionally graded structures. The calculus development, model validation, and result analysis were based on numerical calculus using the finite element method. The utilized models were grounded on the existence of an axial-symmetric plane. So, 2D or 3D simplified models can be used with several variants regarding the mesh fineness. This study results and models are useful to specialists and structure designers of this type, have a high degree of generality, and present opportunities for the application of other calculation methods.

A review on ductile fracture prediction of cracked/notched components: The distinct and simplifying roles of the equivalent material concept and fictitious material concept

Most of engineering structures and components are made of ductile materials, while fracture mechanics tools have been mostly developed for brittle materials. This article investigates the critical load estimation in fracture problems in presence of the elasto-plasticity from the standpoint of major approaches in fracture mechanics including theoretical, experimental, and computational. A review is comprehensively performed on literature with a main focus on two new concepts, namely the Equivalent Material Concept (EMC) and the Fictitious Material Concept (FMC), by which elastoplastic ductile materials can be simplified to linear elastic brittle materials. Therefore, by overcoming the nonlinear aspects, solving of the fracture problems in the linear elastic fracture mechanics (LEFM) framework becomes possible. It is understood from this comprehensive literature survey that while there are several approaches for estimating ductile fracture in cracked/notched members under various loading conditions, most of them need nonlinear analyses, which are typically time-consuming and complicated. It is shown that EMC can work simply and well on those nonlinear materials having small strain-hardening and small/moderate strain-to-failure, while FMC can be effectively and easily applied to nonlinear materials having moderate/great strain-hardening and/or large strain-to-failure, where failure means necking.

Fracture prediction in flat PMMA notched specimens under tension - effectiveness of the equivalent material concept and fictitious material concept

The fracture of notched elements under mode I loading (tension) remains an inexhaustible research topic, especially when it comes to the fracture of thermoplastic materials such as polymethylmethacrylate (PMMA), which experience considerable plastic strains under tension. The paper points out that traditional brittle fracture criteria such as mean stress (MS) or maximum tangential stress (MTS) criteria used to predict this phenomenon do not accurately indicate the value of the critical load. They work much better when combined with the equivalent material concept (EMC) and fictitious material concept (FMC). The effectiveness of both concepts depends on the size of the notch root radius, and thus on the yield zone size.

Effects of copper additives on load carrying capacity and micro mechanisms of fracture in 3D-printed PLA specimens

This study deals with the effects of employing copper additives on the fracture resistance and fracture micro-mechanisms of 3D-printed Polylactic Acid (PLA) specimens under mixed mode I/II loading. Several comparative fracture tests are conducted on pre-cracked Semi-Circular Bend (SCB) specimens made of pure PLA and particulate copper-reinforced PLA (PLA/Cu) printed using the Fused Deposition Modeling (FDM) technique. The SCB specimens are fabricated in three different layer orientations. The comparison of the experimental results reveals that employing copper additives increases the load carrying capacities (LCCs) of the pre-cracked SCB specimens with the flat, on-edge, and upright layer orientations by 2.9%, 15.5%, and 27.7%, respectively. In addition, to determine the tensile properties of two desired materials, dogbone specimens made of PLA and PLA/Cu in three different layer orientations are fabricated and tested. The experimental results obtained from the characterization tests similarly indicate that the presence of copper additives in 3D printed PLA specimens increases ultimate tensile strength by 15.9%, 14%, and, 10.4% in the three flat, on-edge, and upright layer orientations, respectively. Aside from performing experimental tests, the LCCs of pre-cracked specimens are predicted theoretically by utilizing Equivalent Material Concept (EMC) combined with the well-known Average Strain Energy Density (ASED) criterion. It is shown that the EMC-ASED criterion can estimate accurately the experimental LCCs of both FDM-PLA and FDM-PLA/Cu specimens. Finally, the Scanning Electron Microscope (SEM) technique is employed to provide a better understanding of the effects of copper additives on the micro-mechanisms of fracture.

A new strategy for predicting fracture of U‐notched specimens made of Al‐6061‐T6 and Al‐5083 using extended finite element method

AbstractThis research focuses on the numerical investigation of fracture loads of U‐notched specimens made of Al‐6061‐T6 and Al‐5083 under pure opening mode and mixed mode I/II loading conditions. A new methodology is introduced with the aid of the equivalent material concept (EMC) combined with the extended finite element method (XFEM) and linear cohesive zone model (CZM), and the outcomes are compared with a conventional elastic–plastic damage model. The combination of EMC and XFEM result in the numerical EMC‐XFEM model, which provides a fast and accurate method to assess the notch fracture loads and crack growth path. Considering the experimental results, a trial and error loop is performed to calibrate the ductile damage model, which is much more cumbersome than the proposed EMC‐XFEM model. Moreover, the computational cost of elastic–plastic model is much more than the EMC‐XFEM model, although both approaches provide appropriate predictions for fracture of ductile aluminum notches.

Loading rate effects on mixed-mode I/II fracture envelope of epoxy resins with nonlinear behavior

The tangential stress contour (TSC) method in combination with the equivalent material concept (EMC) was used to predict the fracture load, fracture initiation angle, and fracture resistance of an epoxy resin with nonlinear and ductile behavior. In this analysis, both the loading rate and mode mixing effects were taken into account to obtain the fracture envelopes of the tested resin. Based on the considered approach, only a tensile test performed on dogbone specimens and a pure Mode I fracture toughness test using semi-circular bend (SCB) samples are required to predict the ultimate load and crack initiation angle of the resin at different mode mixities. According to this technique, the non-linear ductile behavior of the tested epoxy is simulated by a virtual brittle linear response, which greatly simplifies the problem. The predicted fracture envelope was validated by experimental results. A very good agreement between the prediction and the experimental data was obtained.

Fracture Behavior of AA7075-AA6061 and AA7075-Cu Friction-Stir Welded Joints Containing Blunt V-Notches under Opening-Mode Loading

The purpose of this study is to predict the load-bearing capacity (LBC) of fracture specimens containing V-notched friction-stir welded (FSWed) joints of AA7075-Cu and AA7075-AA6061 materials and subjected to mode I loading conditions. Due to the resulting elastic-plastic behavior and the corresponding development of significant plastic deformations, the fracture analysis of the FSWed alloys requires elastic-plastic fracture criteria, which are complex and time-consuming. Thus, in this study, the equivalent material concept (EMC) is applied, equating the actual AA7075-AA6061 and AA7075-Cu materials to equivalent virtual brittle materials. Then, two brittle fracture criteria, the maximum tangential stress (MTS) and mean stress (MS), are utilized to estimate the LBC of the V-notched FSWed parts. The comparison between the experimental results and the theoretical predictions reveals that both fracture criteria, in combination with EMC, can accurately predict the LBC in the analyzed components.

Investigating the effect of raster orientation on fracture behavior of 3D-printed ABS specimens under tension-tear loading

Most of the engineering components are servicing under complex loading conditions or have complex geometries that lead to a multiaxial stress state in the component. Thus, the fracture behavior of parts under mixed-mode loading conditions should be investigated. The Fused Deposition Modeling (FDM) is a subcategory of the Additive Manufacturing (AM) techniques that has some important manufacturing parameters. The raster orientation (or raster angle) is one of fabricating parameters that significantly affect the mechanical behavior of fabricated parts. Therefore, this study aims to investigate the fracture behavior of FDM specimens made of Acrylonitrile Butadiene Styrene (ABS) under mixed-mode I/III loading conditions. To this goal, four different raster configurations of ψR = 0/90°, 15/-75°, 30/-60°, and 45/-45° were selected for FDM fabrication of edge cracked rectangular specimens, and five loading angles of β = 0° (mode I), 40°, 65°, 72°, and 90° (mode III) were used for performing mixed-mode I/III fracture experiments on the pre-cracked specimens. Besides, some tensile experiments were performed on dog-bone specimens fabricated with the mentioned raster configurations. In order to theoretically predict the failure loads in the tested cracked specimens, a theoretical model named Equivalent Material Concept (EMC) was utilized for equating the ductile behavior of FDM-ABS material with a brittle one. The mentioned concept was coupled with J-integral (EMC-J) and Maximum Tangential Stress (EMC-MTS) criteria to predict the failure loads under mixed-mode loading conditions. The results showed that both EMC-J and EMC-MTS criteria could predict the experimental failure loads well. Additionally, Scanning Electron Microscopy (SEM) was performed on the fracture surfaces to analyze the failure mechanisms of the tested specimens. SEM analysis confirmed the presence of three failure features namely air gaps, filament pullouts, and hackle regions that were discussed comprehensively.

On the combined use of averaged strain energy density criteria (ASED) and equivalent material concept (ECC) for the fracture load prediction of additively manufactured PLA v-notched specimens

On the combined use of averaged strain energy density criteria (ASED) and equivalent material concept (ECC) for the fracture load prediction of additively manufactured PLA v-notched specimens

Uniaxial compression of dry wood: experiment and modeling

The paper considers the dependence of the load on displacement during uniaxial compression of spruce wood samples with an adjustable deformation rate (1 mm/min); the water content in the samples was equal to 6.4%. The study focuses on the analysis of criteria for brittle destruction of wood and its transition to a plastic state. The concept of virtual material transformation (CoViMT) forms the basis of the research. At the idea level, this concept is a variant of the well-known equivalent material concept (EMC). An integral criterion for brittle fracture was developed. Comparison with experimental data showed that the integral criterion and the known differential criterion lead to mismatched points of brittle fracture and transition of wood to the plastic state. Therefore, it is possible to determine the boundaries of the region of plastic states with the help of these criteria. Experiments confirmed the adequacy of the criteria when compressing wood with 6.4% and 18.0% moisture content. However, the volume of studies of the problem touched upon is small, so further research is necessary to better understand the stages of deformation of wood of different species.

Heat treatment effects on fracture resistance of additively manufactured PLA specimens under mode I loading

AbstractThe current paper deals with the influence of heat treatment on the tensile, flexural, and fracture strength of polylactic acid (PLA) specimens made by the fused deposition modeling (FDM) technique. Three different temperatures of 80°C, 100°C, and 120°C were used to anneal the dog bone and enlarged compact tension (ECT) specimens to examine the mechanical and fracture performance of the FDM‐PLA parts, respectively. The fracture behavior was assessed using the equivalent material concept (EMC) combined with the J‐integral, average strain energy density (ASED), and maximum tangential stress (MTS) criteria, and the theoretical estimates were compared with the experimental results. Finally, the effectiveness of these criteria was discussed comprehensively, and the failure mechanisms in the broken tensile and flexural specimens were investigated using scanning electron microscopy (SEM). Overall, applying heat treatment to the FDM specimens could improve their structural integrity by around 57% from the fracture resistance point of view.

Mixed-mode load bearing estimation of the cracked additively manufactured materials using stress/strain-based models

PurposeThe main aim of this study is to investigate the mixed-mode I/II failure and the cracking manner of three-dimensional (3D)-printed components made by the fused deposition modeling technique in an experimental and theoretical manner.Design/methodology/approachAcrylonitrile butadiene styrene (ABS) material and a modified printing method (that increases the adhesion and integrity between the layers and strands) are used for manufacturing the semicircular bending (SCB) test samples. In addition to precracking, the effect of additional stress concentration on the stress field is studied by introducing three small holes to the SCB fracture samples. The critical mixed-mode I/II failure loads obtained from the experiments are predicted using different stress/strain-based fracture theories, including maximum tangential stress (MTS), maximum tangential strain (MTSN), generalized form of MTS and MTSN and combination of them with equivalent material concept (EMC). The effects of plastic deformation, as well as the structural stress concentration, are considered for a more realistic prediction of mixed-mode fracture load.FindingsThe stress-based criteria are more suitable than the strain-based theories. Among the investigated fracture models, the EMC–generalized maximum tangential stress theory provided the best agreement with the experimental results obtained from 3D-printed SCB tests.Originality/valueThe influences of stress risers and applicability of different failure theories in cracked layered 3D-printed parts are studied on the fracture behavior of tested specimens under mixed-mode I/II.

Providing a virtual material for simple estimation of fracture in U-notched highly orthotropic specimens with nonlinear behavior under mixed mode I/II loading

This research investigates the fracture toughness of U-notched Russian pine specimens with highly orthotropic nonlinear behavior under mixed mode I/II loading conditions theoretically and experimentally. The notch strength of orthotropic specimens is successfully predicted by introducing a novel two-step model of material simplification. Adopting this model, the nonlinear orthotropic material is equated with a virtual linear elastic isotropic material by coupling the Virtual Isotropic Material Concept and the Equivalent Material Concept. Therefore, the linear elastic notch fracture mechanics criteria, such as the mean stress and point stress models, can be basically employed to predict the notch fracture toughness of U-notched specimens made of nonlinear orthotropic material. Accordingly, the experimentally obtained notch strength of nonlinear orthotropic samples is predicted in the form of fracture limit curves and the curves of fracture initiation angle. It is shown that the two-step model proposed can be successfully applied for mixed mode I/II fracture estimation of notched orthotropic specimens with nonlinear behavior.