Mean Stress Criteria 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.

Tensile fracture of blunt V-notches in rectangular plates additively manufactured from Acrylonitrile Butadiene Styrene with different raster angles

In this research, the tensile fracture behavior of rectangular specimens made of Acrylonitrile Butadiene Styrene (ABS) containing double-edge blunt V-notches is evaluated. The specimens are printed using the fused deposition modeling (FDM) technique with five different raster angles and three different notch tip radii. To simplify the complex calculations related to the anisotropic behavior of these specimens, the Virtual Isotropic Material Concept (VIMC) is used in conjunction with three well-known linear elastic notch fracture mechanics (LENFM) criteria, i.e., the mean stress (MS), point stress (PS), and averaged strain energy density (ASED) criteria as well as the extended finite element method (XFEM). It is shown that all these fracture models can predict the load-bearing capacity of the 3D-printed notched specimens by acceptable accuracies, where the best predictions belong to the MS criterion with the critical distance obtained directly from the finite element method, and the least accurate predictions belong to the XFEM method.

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.

Fracture assessment of U-notched diagonally loaded square plates additively manufactured from ABS with different raster orientations

This paper investigates the fracture behavior of 3D-printed notched specimens under various combinations of mode I and mode II loadings, including pure mode I and pure mode II loadings. The study employs fused deposition modeling (FDM) to fabricate U-notched diagonally loaded square plate (UNDLSP) specimens using Acrylonitrile Butadiene Styrene (ABS) filaments. To experimentally measure the fracture load and fracture initiation angles, 120 UNDLSP specimens are 3D printed with different notch tip radii, notch orientation angles, and [0, 90], [45, −45] raster orientations. Tensile characteristics and translaminar fracture toughness of ABS plates with [0, 90] and [45, −45] raster orientations are obtained using dog-bone and cracked DLSP samples, respectively. Considering the layered nature and anisotropy of the material, the virtual isotropic material concept (VIMC) is utilized along with two well-known stress-based brittle fracture models: the maximum tangential stress (MTS) and the mean stress (MS) criteria. The test results are predicted using the fracture limit curves and fracture initiation angle curves developed for these fracture models in terms of the notch stress intensity factors (NSIFs). Furthermore, a general equation is established to estimate the fracture initiation angle of U-notched ABS specimens under mixed mode I/II loading, irrespective of geometry, raster orientation, and notch tip radius, based on the curves obtained from the MTS and MS criteria. The fracture surfaces of the UNDLSP specimens are examined using scanning electron microscopy (SEM) to study the micro-mechanisms involved in the fracture process. The findings indicate that both the VIMC-UMTS and VIMC-UMS criteria accurately predict the experimentally achieved fracture loads. Additionally, it is observed that the fracture initiation angle curves for both criteria are nearly identical and accurate. The significance of this research is not only providing numerous new experimental results on mixed mode I/II fracture of notched 3D-printed ABS plates, but also providing simple, fast, accurate, and robust criteria for predicting the critical loads of such plates, without the need for conducting layer-by-layer failure analysis using progressive damage models.

VO-Notches Subjected to Tension-Torsion Loading: Experimental and Theoretical Fracture Study on Polymeric Samples.

In this research, the fracture behavior of brittle specimens weakened by V-shaped notches with end holes (VO-notches) is studied. First, an experimental investigation is conducted to evaluate the effect of VO-notches on fracture behavior. To this end, VO-notched samples of PMMA are made and exposed to pure opening mode loading, pure tearing mode loading, and some combinations of these two loading types. As part of this study, samples with end-hole radii of 1, 2, and 4 mm are prepared to determine the effect of the notch end-hole size on the fracture resistance. Second, two well-known stress-based criteria, namely the maximum tangential stress (MTS) criterion and the mean stress (MS) criterion, are developed for VO-shaped notches subjected to mixed-mode I/III loading, also determining the associated fracture limit curves. A comparison between the theoretical and the experimental critical conditions indicates that the resulting VO-MTS and VO-MS criteria predict the fracture resistance of VO-notched samples with about 92% and 90% accuracy, respectively, confirming their capacity to estimate fracture conditions.

Mechanical aspects of semi-circular sandstone fractured specimens with U-notch in the presence of various bedding angles

In tunnel and underground structures, the deformation and damage of layered rock masses often exhibit substantial anisotropy, where the fracture pattern of layered rock masses containing notched cracks directly influences the construction stability of the project. By this virtue, this paper presents a theoretical formulation of the fracture toughness of anisotropic rock materials containing U-notches on the basis of the constitutive model of transversely isotropic materials. The anisotropic influence coefficients are also appropriately incorporated into the formulas of the point stress (PS) and mean stress (MS) criteria to obtain their corresponding modified relations. The fracture toughness (KIC) of sandstones with bedding angles is evaluated by utilizing semi-circular bend (SCB) and U-notched semi-circular bend (USCB) specimens. The theoretically obtained results and experimentally observed data display that the fracture toughness of the specimens gradually decreases with increasing bedding angle, irrespective of the notch tip radius. Further, the results of the mean stress criterion are closer to the experimental data in comparison with those of the point stress criterion. Additionally, the fracture damage patterns pertinent to the SCB and USCB sandstone specimens with various bedding angles are displayed and discussed. The achieved results could provide a solid basis for better realizing the engineering deformations and failure analyses of layered sandstones.

Mixed-mode fracture prediction of acrylonitrile butadiene styrene material fabricated via fused deposition modeling

Fused deposition modeling is one of the additive manufacturing techniques that is used for rapid manufacturing and prototyping, in various industries. Due to the layer-wise fabrication routine in the fused deposition modeling process, the final fabricated products often show anisotropic behavior. As a result, to investigate the mechanical performance of the three-dimensional-printed parts, complex and time-consuming analyses are required. The main purpose of the current research paper is to determine whether the isotropic assumption of material using maximum tangential stress and mean stress criteria is capable of predicting the mixed-mode fracture resistance of the three-dimensional -printed parts. Here, three different building conditions are considered for fabricating tensile and fracture specimens, and various mechanical and fracture characteristics are evaluated. Finite element simulations of the test specimens are executed and the stress results are used as input for fracture prediction of the fused deposition modeling parts. Two different cases are considered for isotropic assumptions wherein the first case (case A), each fracture specimen is modeled by using its own direct mechanical properties. While in the second case (case B), the average mechanical properties are used for modeling the cracked specimens. The results showed that both maximum tangential stress and mean stress criteria can predict the fracture loads of the fused deposition modeling parts, without the need for complex and time-consuming analyses associated with fully anisotropic materials. In addition, an improvement of the predictions was observed while using case A compared to case B.

Mixed mode I-III fracture resistance of stainless steel 316L weakened by V-notches with end holes

Notch fracture resistance of stainless steel 316L is investigated under mixed-mode I/III loading. A previously proposed test fixture, utilized in the past for testing low/medium toughness polymeric and metallic materials, is first modified to make it appropriate for testing significantly tough materials like stainless steel 316L. Then, original fracture tests are carried out on a specific sample weakened by V-notches with end holes (VO-notches) and loaded under different combinations of tension and out-of-plane shear, from which the critical loads and the fracture behaviour are extracted. Due to great strain-hardening and significant strain-to-failure for stainless steel 316L, the Fictitious Material Concept (FMC) is first employed to avoid complexities associated with fracture prediction. Then, FMC is combined with the maximum tangential stress (MTS) and mean stress (MS) criteria to predict the notch fracture toughness values determined experimentally. With approximately 87 % and 86 % accuracy in estimation of the mean experimental results, both combined criteria, called FMC-MTS and FMC-MS, are revealed to be successful.

Tensile-Tearing Fracture Analysis of U-Notched Spruce Samples.

Spruce wood (Picea Mariana) is a highly orthotropic material whose fracture behavior in the presence of U-shaped notches and under combined tensile-tearing loading (so-called mixed-mode I/III loading) is analyzed in this work. Thus, several tests are carried out on U-notched samples with different notch tip radii (1 mm, 2 mm, and 4 mm) under various combinations of loading modes I and III (pure mode I, pure mode III, and three mixed-mode I/III loadings), from which both the experimental fracture loads and the fracture angles of the specimens are obtained. Because of the linear elastic behavior of the spruce wood, the point stress (PS) and mean stress (MS) methods, both being stress-based criteria, are used in combination with the Virtual Isotropic Material Concept (VIMC) for predicting the fracture loads and the fracture angles. By employing the VIMC, the spruce wood as an orthotropic material is modeled as a homogeneous and isotropic material with linear elastic behavior. The stress components required for calculating the experimental values of notch stress intensity factors are obtained by finite element (FE) analyses of the test configuration using commercial FE software from the fracture loads obtained experimentally. The discrepancies between the experimental and theoretical results of the critical notch stress intensity factors are obtained between −12.1% and −15% for the PS criterion and between −5.9% and −14.6% for the MS criterion, respectively. The discrepancies related to fracture initiation angle range from −1.0% to +12.1% for the PS criterion and from +1.5% to +12.2% for the MS criterion, respectively. Thus, both the PS and MS models have good accuracy when compared with the experimental data. It is also found that both failure criteria underestimate the fracture resistance of spruce wood under mixed-mode I/III loading.

A two-level strategy for simplification of fracture prediction in notched orthotropic samples with nonlinear behavior

In this paper, the load bearing capacity of U-notched specimens made of Russian pine wood, as a natural orthotropic material with nonlinear behavior, is investigated under pure mode I loading. The load bearing capacity of the orthotropic specimens with nonlinear behavior is predicted adopting a novel combination of the Equivalent Material Concept (EMC) and the Virtual Isotropic Material Concept (VIMC) in conjunction with the brittle failure criteria. By applying the EMC, the orthotropic material with nonlinear behavior is equated with a virtual linear one. Subsequently, using the VIMC, the orthotropic material with linear behavior obtained from the previous step is equated with a virtual isotropic material with linear behavior. Eventually, the load bearing capacity of the orthotropic nonlinear notched samples is predicted using two common brittle failure criteria, so-called the point stress criterion and the mean stress criterion. It is shown that both criteria employed for predicting the notch fracture toughness of the wood specimens are of good accuracy.

A Modified Mean Stress Criterion for Considering Size Effects on Mode I Fracture Estimation of Rounded-Tip V-Notched Polymeric Specimens.

The aim of this paper is to assess the size and geometry effects on the mode I notch fracture toughness of polymeric samples containing rounded-tip V-shaped (RV) notches (V-notch with a finite radius at the notch tip). First, using a large number of fracture tests on an RV-notched Brazilian disk and semi-circular bending polymeric samples with four different sizes, the size-dependent values of the notch fracture toughness are obtained. Then, the mean stress criterion is modified for characterizing the size-dependency of notch fracture toughness in polymeric samples. The resulting modified mean stress criterion considers higher order terms of the stress field when calculating the fracture process zone length around the tip of the defect. Additionally, the critical distance rc is assumed to be associated with the specimen size and a formula containing fitting parameters is utilized for considering this trend of rc. The comparison between the values of notch fracture toughness obtained from experiments and those predicted by the modified mean stress criterion shows that the suggested approach can provide accurate estimations of size-dependent values of notch fracture toughness in polymeric specimens containing RV notches.

Translaminar notch fracture toughness expressions for composite laminates

First, two different test specimens, namely the rectangular tension (RT) and semi-circular bend (SCB) specimens, weakened by U-notches of various notch tip radii and made of E-glass/epoxy composite laminates of different lay-up configurations, are considered for measuring experimentally the translaminar notch fracture toughness (TLNFT) of the composite material under pure mode I loading conditions. Then, two new closed-form expressions are proposed for the TLNFT, by taking advantages of the maximum tangential stress (MTS) and the mean stress (MS) criteria, as well as the recently proposed virtual isotropic material concept (VIMC), with the goal to estimate the experimental results. It is found that both criteria can well estimate the test results that locate always between the predictions of MTS and MS criteria. Taking into account that MTS criterion is more conservative and simpler than MS criterion, it is preferred in mechanical design of notched E-glass/epoxy composite structures.

Elastoplastic fracture analysis of thin notched AA7075‐AA2024 dissimilar friction‐stir‐welded plates under mixed mode I/II loading

AbstractIn this research, fracture of friction‐stir welding (FSW) of AA2024‐T3 and AA7075‐T6 aluminum alloys weakened by notches is studied. In the experimental part, a rectangular specimen, called U‐notched diagonally loaded square plate (UNDLSP) and made of welded AA2024‐T3 and AA7075‐T6 aluminum alloys, is used for fracture tests under pure mode I and mixed mode I/II loading conditions. For fracture tests, different notch tip radii and different ratios of loading mode combinations are considered. In the theoretical part, due to ductility of the material under test, combination of the equivalent material concept (EMC) with two brittle fracture criteria (maximum tangential stress and mean stress criteria) is used to predict the load‐bearing capacity (LBC) of the samples. By comparing the experimental and theoretical results, it is revealed that both criteria in combination with EMC are able to predict the LBC of the U‐notched samples well and with high accuracy.

Fracture testing and estimation of critical loads in a PMMA-based dental material with nonlinear behavior in the presence of notches

The goal of the present investigation is twofold: first, to provide new experimental data on the fracture behavior of biopolymer specimens containing notches, and second, to validate new fracture criteria to predict the corresponding experimental fracture loads. For this purpose, nine fracture experiments are conducted on U-notched rectangular specimens with different notch tip radii made of polymer-based dental material under monotonic tension. As the main outcomes of the experimental program, the fracture loads of the specimens, as well as the corresponding load-displacement curves, were recorded. Due to the nonlinear behavior of the dental material being tested, considerable plastic deformations are developed in the U-notch vicinity and, hence, the use of linear elastic notch fracture mechanics (LENFM) criteria (e.g., the maximum tangential stress (MTS) and mean stress (MS) criteria) for fracture (critical) load predictions provides inaccurate results. Consequently, the Equivalent Material Concept (EMC), which equates the nonlinear biopolymer material with a virtual brittle material having perfectly linear elastic behavior, is combined with the MTS and the MS criteria, allowing the use of LENFM for fracture load predictions of the U-notched biopolymer specimens being tested. It is observed that the two resulting criteria, EMC-MTS and EMC-MS, provide very good predictions of the experimental results. From the viewpoint of mechanical design, the EMC-MTS criterion may be preferred to the EMC-MS criterion, given its inherent simplicity.

Experimental study on dynamic notch fracture toughness of V-notched rock specimens under impact loads

In this study, the dynamic notch fracture toughness of V-notched rock specimens was investigated. V-notched semicircular bend specimens made of a medium-grained granitic rock called Fangshan granite were subjected to tests using a split Hopkinson pressure bar (SHPB) system combined with an ultrahigh-speed camera. First, an empirical formula was derived using dimensional analysis to calculate the fracture parameters of sharp V-notches, and the dynamic notch fracture toughness was calculated using dynamic forces obtained from the SHPB tests and the empirical formula. Second, full-field displacement fields generated during the dynamic fracture process were measured using the digital image correlation (DIC) method, and the notch fracture toughness was extracted using the displacement fields at the V-notch tip. Third, the experimental results obtained using the empirical formula were compared with the DIC results and subsequently validated using a modified mean stress criterion. The proposed methods have significant applications in the fracture assessment of rock structures weakened by notches.

Compressive fracture analysis of U-notched specimens made of porous graphite reinforced by aluminum particles

Brittle fracture in U-notched specimens made of porous graphite reinforced by aluminum particles is experimentally and theoretically investigated under compressive loading conditions, i.e. the closing mode loading. Using fracture tests, the critical loads of such specimens are experimentally acquired. Then, the maximum tangential stress and the mean stress criteria are used with the critical parameters obtained from an experimental calibration for predicting the critical loads of the specimens theoretically; showing great agreement with the experimental results. After that, the compressive critical stress of the reinforced porous graphite is theoretically estimated by means of the Equivalent Material Concept and used inside the two criteria for theoretical predictions. Referring to the successful joint of this concept with the criteria mentioned above, it is revealed that this concept is a strong tool for estimating the compressive critical stress of graphite materials without the need for experimental calibration.

DEM investigation on the breakage of spherical aggregate under multi‐contact loadings

AbstractParticle crushing is commonly encountered during the storage, transportation, and handling of granular assemblies. This work is aimed at ascertaining the applicability of four particle breakage criteria frequently mentioned in literature. Discrete element method (DEM) simulations were conducted to investigate the crushing of spherical aggregates under multicontact loadings. Mean and major principal stress criteria, octahedral shear stress criterion, and maximal contact force (MCF) criterion were then evaluated based on the obtained DEM results. It is found that the first three parameters all vary with the number of loading contacts, demonstrating they cannot predict the crushing of particles under arbitrary loading configuration. Simulation results indicate that the MCF at crushing is related to the number and the spatial arrangement of loading contacts. Thus, strictly speaking, this parameter cannot uniquely define particle breakage either. The influences of the microstructural heterogeneity on the breakage strength of particle and also on the applicability of MCF criterion are discussed.

Extension of the Equivalent Material Concept to Compressive Loading: Combination with LEFM Criteria for Fracture Prediction of Keyhole Notched Polymeric Samples

This work analyzes, both theoretically and experimentally, the fracture process of square specimens weakened by keyhole notches and subjected to compressive stresses. Two materials are covered: general-purpose polystyrene (GPPS) and poly(methyl methacrylate) (PMMA). Firstly, the load-carrying capacity (LCC) of the specimens is determined experimentally. Then, by using the equivalent material concept (EMC) for compressive conditions coupled with the maximum tangential stress (MTS) and the mean stress (MS) criteria, the LCC of the notched specimens is predicted. The results show that by using the approach proposed in the present investigation, not only can the critical loads in the keyhole notched polymeric specimens be precisely predicted, but also the corresponding compressive critical stress of the two mentioned polymers can be successfully estimated.

Notch Fracture in Polymeric Specimens under Compressive Stresses: The Role of the Equivalent Material Concept in Estimating the Critical Stress of Polymers

In this paper, the fracture of notched polymeric specimens under compressive stresses was investigated both experimentally and theoretically. In the experimental section, to determine the load-carrying capacity (LCC) of U-notched specimens made of general-purpose polystyrene (GPPS) and polymethyl-methacrylate (PMMA) polymers, tests were performed on notched square samples under compression, i.e., negative mode I loading. In the observation of the nonlinear behavior of the two polymers in the standard compressive tests, for the first time, the equivalent material concept (EMC) was used under compressive loading to theoretically estimate the critical stresses of the two polymers, which were shown to be significantly different from the ultimate strengths obtained from the standard compression tests. By linking the EMC to the maximum tangential stress (MTS) and mean stress (MS) criteria, the LCC of the notched specimens was predicted. The outcomes are twofold: First, MTS, MS, EMC–MTS, and EMC–MS criteria provide accurate predictions of the experimental critical loads observed in the U-notched polymeric specimens; second, the combination of the EMC with the MTS and MS criteria, allow such predictions to be obtained without any need for experimental calibration.

Fracture Behavior of Two Biopolymers Containing Notches: Effects of Notch Tip Plasticity

This paper analyzes the notch effect on the fracture behavior of two biomaterials (a brittle bone cement and a ductile dental material) under mode I loading. U-notched Brazilian disk (UNBD) specimens of both materials were tested under remote compression, determining the corresponding fracture loads and load-displacement curves. Additionally, cracked rectangular and semicircular bend (SCB) specimens were tested under symmetric three-point bending in order to determine the fracture toughness of the two materials. Then, fracture loads were derived theoretically by applying the maximum tangential stress (MTS) and the mean stress (MS) criteria. Due to the brittle linear elastic behavior of the bone cement material, the MTS and MS criteria were directly applied to this material; however, given the significant nonlinear behavior of the dental material, the two fracture criteria were combined with the Equivalent Material Concept (EMC) for the fracture analyses of the dental material specimens. The results reveal a very good accuracy of both the MTS and the MS criteria for the fracture analysis of bone cement notched specimens. In the case of the dental material, very good results are also obtained when combining the MTS and the MS criteria with the EMC. The proposed approach can be useful for the fracture analysis of a wide range of biopolymers, from brittle to ductile behavior.