Mixed mode fracture investigation of rock specimens containing sharp V-notches

This work aims to assess both experimentally and analytically the fracture behavior of rock specimens containing sharp V-notches (SV-notches) subjected to mixed mode I/II loading. To this end, firstly, several mixed mode fracture tests were conducted on Brazilian disk specimens weakened by an SV-notch (SVNBD sample), performed in their corresponding center and with various notch opening angles. Secondly, the fracture resistance of the tested samples was predicted using a criterion named MTS-FEM. This approach is based on the maximum tangential stress (MTS) criterion, in which the tangential stress is determined from the finite element method (FEM). Additionally, in the present research, the required critical distance is calculated directly from finite element analyses performed on cracked samples. Comparing the experimental results and the analytical predictions, it is shown that the fracture curves obtained from the MTS-FEM criterion are in agreement with the experimental results. These results are achieved without the need for the calculation of stress series expansion coefficients, as an additional advantage of the proposed approach

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

ABSTRACT: 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

Critical Load Prediction in Notched E/Glass-Epoxy-Laminated Composites Using the Virtual Isotropic Material Concept Combined with the Average Strain Energy Density Criterion

ABSTRACT: This paper attempts to validate the application of the Virtual Isotropic Material Concept (VIMC) in combination with the average strain energy density (ASED) criterion to predict the critical load in notched laminated composites. This methodology was applied to E/glass-epoxy-laminated composites containing U-notches. For this purpose, a series of fracture test data recently published in the literature on specimens with different notch tip radii, lay-up configurations, and a number of plies were employed. It was shown that the VIMC-ASED combined approach provided satisfactory predictions of the last-ply failure (LPF) loads (i.e., critical loads)

Tensile-Tearing Fracture Analysis of U-Notched Spruce Samples

ABSTRACT: 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 mixedmode 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 mixedmode I/III loading

A Methodology to Determine the Effective Plastic Zone Size Around Blunt V-Notches under Mixed Mode I/II Loading and Plane-Stress Conditions

ABSTRACT:The determination of the ductile failure behavior in engineering components weakened by cracks and notches is greatly dependent on the estimation of the plastic zone size (PZS) and, particularly, the effective plastic zone size (EPZS). Usually, time-consuming complex elastic-plastic analyses are required for the determination of the EPZS. Such demanding procedures can be avoided by employing analytical methods and by taking advantage of linear elastic analyses. In this sense, this work proposed a methodology for determining the PZS around the tip of blunt V-notches subjected to mixed mode I/II loading and plane-stress conditions. With this aim, firstly, existing approximate mathematical expressions for the elastic stress field near round-tip V-notches reported in the literature are presented. Next, Irwin's approach (fundamentally proposed for sharp cracks) and a yield criterion (von Mises or Tresca) were applied and are presented. With the aim of verifying the proposed methodology, elastic-plastic finite element analyses were performed on virtual AISI 304 steel V-notched specimens. It was shown that the analytical formulations presented cannot estimate the complete shape of the plastic zone. However, the EPZS, which is crucial for predicting the type of ductile failure in notched members, 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

ABSTRACT: n 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 Load Predictions in Short Glass Fiber Reinforced Polyamide 6 U-Notched Specimens Combining the Equivalent Material Concept and the Theory of Critical Distances

ABSTRACT: This article provides the prediction of fracture loads in single edge notched bending (SENB) specimens made of short glass fiber reinforced polyamide 6 (SGFR-PA6) and containing U-notches. The predictions are obtained through the combination of the equivalent material concept and the theory of critical distances (TCD). The latter is based on the material critical distance (L) and has a linear-elastic nature. This implies that in those materials exhibiting non-fully linear-elastic behavior, the determination of the material critical distance requires a calibration process that may be performed by fracture testing on notched specimens or through a combination of fracture testing and finite elements simulation. This represents a significant barrier for the application of the TCD on an industrial level. The proposed methodology defines an equivalent linear-elastic material on which the TCD may be applied through its basic formulation and without any previous calibration of the corresponding critical distance. It is applied to SGFR-PA6 SENB specimens, providing accurate predictions of the experimental fracture loads.The authors of this work would like to express their gratitude to the Spanish Ministry of Science and Innovation for the financial support of the project MAT2014-58443-P: “Análisis del Comportamiento en Fractura de Componentes Estructurales con Defectos en Condiciones de Bajo Confinamiento Tensional,” on the results of which this article is based

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

ABSTRACT: 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

Estimation of Fracture Loads in AL7075-T651 Notched Specimens Using the Equivalent Material Concept Combined with the Strain Energy Density Criterion and with the Theory of Critical Distances

The main goal of this paper is the application of the Strain Energy Density (SED) criterion and the Theory of Critical Distances (TCD), both of them in combination with the Equivalent Material Concept (EMC), to predict the fracture loads of aluminum alloy Al7075-T651 Compact Tension (CT) specimens containing U-shaped notches. For this purpose, 45 fracture tests were performed combining two rolling orientations (transverse and longitudinal) and 6 notch radii, which cover from crack-type defects (0 mm) up to 2 mm-notch radius. Crack-type specimens are used to define the fracture properties of the material and the rest of the tests are used to check and compare the experimental fracture loads with the loads predicted using the different aforementioned criteria: SED, EMC-SED and EMC-TCD. The theoretical results of the fracture load predictions for the virtual brittle material obtained employing the EMC are in good agreement with the experimental results reported for real samples.The authors of this work would like to express their gratitude to the Spanish Ministry of Science and Innovation for the financial support of the Project MAT2014-58443-P: “Análisis del comportamiento en fractura de componentes estructurales con defectos en condiciones debajo confinamiento tensional”, on the results of which this paper is based

The Effect of Noise on the Dirac Phase of Electron in The Presence of Screw Dislocation

The effect of noise on the Dirac phase of electron in the presence of screw dislocation is studied. An uncorrelated noise, which coincides with the nature of thermal fluctuations, is adopted. Results indicate that the Dirac phase is robust against existing noise in the system