Single Edge Notch Bend Specimens Research Articles

Determination of Constraint-Modified J-R Curves for Carbon Steel Storage Tanks

Mechanical testing of A285 carbon steel, a storage tank material, was performed to develop fracture properties based on the constraint theory of fracture mechanics. A series of single edge-notched bend (SENB) specimen designs with various levels of crack tip constraint were used. The variation of crack tip constraint was achieved by changing the ratio of the initial crack length to the specimen depth. The test data show that the J-R curves are specimen-design-dependent, which is known as the constraint effect. A two-parameter fracture methodology is adopted to construct a constraint-modified J-R curve, which is a function of the constraint parameter, A2, while J remains the loading parameter. This additional fracture parameter is derived from a closed form solution and can be extracted from the finite element analysis for a specific crack configuration. Using this set of SENB test data, a mathematical expression representing a family of the J-R curves for A285 carbon steel can be developed. It is shown that the predicted J-Rcurves match well with the SENB data over an extensive amount of crack growth. In addition, this expression is used to predict the J-R curve of a compact tension specimen (CT), and reasonable agreement to the actual test data is achieved. To demonstrate its application in a flaw stability evaluation, the configuration of a generic A285 storage tank with a postulated axial flaw is used. For a flaw length of 10% of the tank height, the predicted J-R curve is found to be similar to that for a SENB specimen with a short notch, which is in a state of low constraint. This implies that the use of a J-R curve from the ASTM (American Society for Testing and Materials) standard designs, which typically are high-constraint specimens, may be overly conservative for analysis of fracture resistance of large structures.

Effect of cooling rate on fracture behavior of polypropylene

The purpose of this work is to investigate the influence of morphology, induced by cooling rate during molding, on the time–temperature dependence of fracture behavior of polypropylene (PP). Fractures tests were performed over a range of loading rates from 0.2 mm/min to 2.5 m/s, using the single edge notched bending specimen. The results show that the transition temperature from brittle to ductile behavior increases with decreasing cooling rate. However, at very low loading speed (0.2 mm/min), an opposite effect is observed, the brittle–ductile transition temperature diminishes with lower cooling rate. At low test speeds, the fracture performance is reduced with a decreasing cooling rate. Conversely, under impact, the fracture toughness of PP is enhanced with a decrease in cooling rate. This is explained by the mechanism of blunting of the crack tip due to adiabatic heating under high loading rates. The blunting effect results in a more significant plastic deformation of the crystalline region that requires a higher energy. The brittle–ductile transition was characterized by an energy activation process expressed by the Arrhenius equation. Decreasing the cooling rate results in a decrease of both the pre-exponential factor and the energy barrier controlling the time–temperature dependence of fracture behavior. The reduction of the pre-exponential factor corresponds to a more ordered morphology due to a reduction in the entropy and is consistent with a higher crystallinity. The reduction of activation energy with higher crystalline level suggests that the brittle–ductile transition also involves the primary relaxation process that is known to occur mostly in an amorphous structure. A higher crystallinity would restrain the primary relaxation processes and the brittle–ductile transition becomes more dependent on the secondary movements of the chain segments. The results demonstrate that the relationship between deformation rate, temperature, and mechanical performance of PP is not only controlled by molecular relaxation processes, but also strongly dependent on its morphology.

Fracture toughness of rubber-modified epoxy adhesives: effect of plastic deformability of the matrix phase

The fracture toughness of adhesively bonded compact tension (CT) and bulk single-edge notched bend (SENB) specimens using rubber-modified epoxy resins was investigated in terms of the relation between the J-integral value and crack extension, whereby the rubber-modified epoxy resins allow to alter the plastic deformability by changing curing temperature. For the SENB specimen, the crack extension is very small and the J-integral value increases with enhanced plastic deformability. On the other hand, for the CT specimen, a considerable crack extension is observed, furthermore, when the crack extension is nearly equal to 0.2 mm, the J-integral value does not vary with curing temperature; however, the slope of the J–Δ a curve slightly decrease with enhanced plastic defomablity. To elucidate these behaviors, assuming that the resins are governed by the Gurson's constitutive equation, the void–volume fractions near the crack tip of both the specimens were calculated by finite element method. It was found that the characteristics of J–R curves can be explained from the results of calculated void–volume fraction.

Fracture behaviour of diffusion bonded titanium alloys with strength mismatch

The present study considers the effect of strength mismatch on the fracture behaviour of diffusion bonded joints between commercially pure (CP) Ti and Ti-6Al-4V (Ti64), including dissimilar joints and sandwich structures with strength undermatching and overmatching. The aim of the investigation is to determine the influence of the interlayer thickness (for both higher and lower strength interlayers) and the bond quality on the deformation behaviour and fracture toughness of the joints. The influence of mechanical heterogeneity (strength mismatch) on the fracture behaviour of the interface in dissimilar joints was also investigated. Round bars of CP Ti and Ti64 having a diameter of 40 mm were diffusion bonded as dissimilar butt joints and sandwich structures containing lower strength (undermatching) and higher strength (overmatching) interlayers of different thicknesses. Round transverse tensile specimens and standard four point bend (single edge notch bend) specimens were extracted from the joints via spark erosion cutting. The four point bend specimens were fatigue precracked to introduce a sharp crack after introducing machine notches at the centre of the interlayers in the sandwich structures and at the interface in the dissimilar joints, and tested at room temperature. Some specimens were also prepared with the crack positioned away from the interface to determine the effect of notch position on fracture behaviour. The effect of strength mismatch on the crack tip opening displacement fracture toughness parameter of the joints has been evaluated. Crack initiation, crack growth, and crack deviation processes have been examined and fracture resistance curves (R curves) constructed for the joints. These results were used to explain the influence of mechanical heterogeneity of the joints and interlayer thickness on fracture behaviour.

Mode Mixity and Crack Tip Yield Zones in TSD Sandwich Specimens with PVC Foam Core

In an effort to examine the relation between core fracture toughness and face/core debond toughness, fracture mechanics analysis was conducted on core and debond fracture specimens. H30, H80, H100, H200 and R400 PVC foam cores were examined. Stress intensity factors and size of the plastic zone around the crack tip in foam core Single-Edge Notch Bend (SENB), and Tilted Sandwich Debond (TSD) specimens with foam core were estimated from the elastic displacement and stress fields near the crack tip. Analysis of the influence of core thickness and crack depth on the plastic zone size was performed on TSD specimens with H100 and R400 cores. It was found that the crack loading in the TSD specimen is essentially mode I, and that shear loading is not a factor explaining the higher debond than core toughness. At onset of fracture, the plastic zone height in the TSD specimen is much larger than that in a corresponding foam SENB specimen. It is believed that the plastic zone enlargement is a major factor explaining the elevation of debond toughness over the core toughness.

Fatigue Crack Growth in Cantilever Bending Under Displacement Control

Abstract Fatigue crack growth (FCG) behavior of two martensitic steel grades was investigated using a single edge-notched bend specimen fixed beyond the notched section in cantilever bending under displacement control. This task was made possible by a new and original testing methodology developed on the basis of finite element analyses to define valid boundary conditions and the corresponding stress intensity factor K-expression for the test specimen. The behavior has been described including the nearthreshold zone and the second zone of relatively high FCG rates. Results for the two steel grades were found to correspond well with the empirical models reported in the literature. This confirms the validity of the methodology proposed in the present paper, which can be attributed to: (1) the accurate K-expression for the test specimen, (2) the proper definition of the boundary conditions adopted during testing, and (3) the validity of the adopted boundary conditions.

Micromechanical modeling of fracture initiation in 7050 aluminum

Mechanical testing and finite element calculations have been carried out to characterize the fracture initiation behavior of the high-strength aluminum alloy 7050-T7451. Results show that fracture initiation is well predicted for two specimen types of differing constraint using the stress-modified, critical plastic strain micromechanical model. The relation between stress triaxiality and critical plastic strain was found from a series of notched tensile specimens. Data from these tests are interpreted using both companion finite element modeling and common, semi-empirical relations, and these two approaches are compared. Multiple, interrupted tests of standard, highly constrained single edge notched bend specimens are used to obtain the J– R curve in 7050 for small amounts of tearing to experimentally identify initiation. Companion modeling and the stress-modified, critical plastic strain relation are used to find the length scale for fracture, l ∗ , needed for initiation predictions. The calibrated stress-modified, critical plastic strain relation and length scale are then used to predict fracture initiation of a low-constraint specimen. The prediction is within 5% of the experimental measurements. Finally, various aspects of the procedure followed in the present work are compared to previous efforts using similar approaches.

The fracture behaviour of cast steel and its prediction based on the local approach

The master curve (MC) concept has been used for assessment of the fracture toughness transition behaviour of C–Mn cast steel intended for fabrication of large containers for spent nuclear fuel (ŠKODA). Standard fracture toughness tests using single edge notched bend specimens (SENB) with various crack lengths, the static tests of the CVN specimens and the axisymmetric notched tensile specimens have been utilised. The transferability of results received on the small pre-cracked Charpy specimens are tested here and the methodology MC is applied. For determining the reference transition temperature, T o, which is taken as a basic material characteristic positioning the MC on the temperature axis, the large (1T) specimens are required. Additionally, the small pre-cracked Charpy-type specimens have been used for determining the fracture transition behaviour and for fracture toughness measurement and prediction.

Fracture testing and finite element modeling of pure titanium

This paper presents the results of fracture experiments and corresponding finite element analyses (FEA) of pure titanium. This investigation was motivated by the desire to develop a J– R testing protocol and numerical procedures that are applicable to a titanium/titanium boride layered functionally graded material. Tensile tests and a two-dimensional axisymmetric finite element model were used to determine the plasticity data for the titanium. Crack growth experiments were conducted in three-point bending using single edge notched bend specimens. Three-dimensional FEA of crack growth initiation and two-dimensional FEA with automatic crack propagation were performed. Two crack propagation conditions based on experimental data were used: (a) crack length versus load-line displacement and (b) crack length versus crack mouth opening displacement. The subsequent predictions of the non-linear finite element models are in reasonable agreement with the measured value of J at initiation and with the rising J– R data during crack propagation.

Fracture toughness characterizations of compatibilized polyamide-6 (PA6)/poly(phenylene ether) (PPE) blends

Under the plane-strain condition, the material properties, KIC and GIC, of the blends, brittle or with small-scale yielding, increase with increasing elastomer content. To evaluate the critical J-integral for the ductile blends, several methods have been compared to understand the influence of elastomer content and different thicknesses using single-edge notch-bend specimens. For a given thickness, the fracture toughness increases with increasing elastomer content. Moveover, the slope of the R-curve becomes gradually steeper with increasing elastomer content and decreasing specimen thickness. JIC values determined from ASTM E813-89 and modified ASTM E813-81 methods always give the highest and the lowest values, respectively. JIC values determined from three other methods are comparable and can be employed to characterize the fracture toughness of the compatibilized PA6/PPE blends. It is noted that JIC values determined from the modified ASTM E813-89 and the hysteresis energy methods are apparently independent of thickness. Therefore, these two methods may be considered as potential alternative techniques to evaluate the critical J-integral for toughened polymer blends.

J–R curves corrected by load-independent constraint parameter in ductile crack growth

The constraint effect on J–resistance curves of ductile crack growth is considered under the condition of two-parameter J–Q* controlled crack growth, where Q* is a modified parameter of Q in the J–Q theory. Both J and Q* are used to characterize the J–R curves with J as the loading level and Q* as a constraint parameter. It is shown that Q* is independent of applied loading under large-scale yielding or fully plastic deformation, and so Q* is a proper constraint parameter during crack growth. An approach to correct constraint effects on the J–R curve is developed, and a procedure of transferring the J–R curves determined from standard ASTM procedure to nonstandard specimens or real cracked structures is outlined.The test data of fracture toughness, JIC, and tearing modulus, TR, by Joyce and Link (Engng. Fract. Mech. 57(4) (1997) 431) for a single-edge notched bend specimen with various depth cracks are employed to demonstrate the efficiency of the present approach. The variation of JIC and TR with the constraint parameter Q* is obtained, and then a constraint-corrected J–R curve is constructed for the test material of HY80 steel. Comparisons show that the predicted J–R curves can match well with the experimental data for both deep and shallow cracked specimens over a reasonably large amount of crack extension.Finally, the present approach is applied to predict the J–R curves of ductile crack growth for five conventional fracture specimens. The results show that the effect of specimen geometry on the J–R curves is generally much larger than the effect of specimen sizes, and larger specimens tend to have lower crack growth resistance curves.

Fracture and fatigue properties of acrylic bone cement: The effects of mixing method, sterilization treatment, and molecular weight

The purpose of this study was to characterize the relative and combined effects of sterilization, molecular weight, and mixing method on the fracture and fatigue performance of acrylic bone cement. Palacos® R brand bone cement powder was sterilized using ethylene oxide gas (EtO) or gamma irradiation. Nonsterile material was used as a control. Molecular weights of the bone-cement powders and cured cements were measured using gel permeation chromatography. Hand and vacuum mixing were employed to mold single edge-notched bend specimens for fracture toughness testing. Molded dog-bone specimens were used for fatigue tests. Electron microscopy was used to study fracture mechanisms. Analysis of variance and Student t-tests were used to compare fracture and fatigue performance between sterilization and mixing groups. Our results indicate that vacuum mixing improved significantly the fracture and fatigue resistance (P <.05, P <.07) over hand mixing in radiation-sterilized and EtO-sterilized groups. In vacuum-mixed cement, the degradation in molecular weight resulting from gamma irradiation decreased fracture resistance significantly when compared with EtO sterilization and control (P <.05). A corresponding decrease in fatigue resistance was observed in the cement that was degraded severely by a radiation dose of 10 MRad (P <.05). In contrast, EtO sterilization did not result in a significantly different fracture resistance when compared with unsterilized controls for vacuum-mixed cement (P >.1). For hand-mixed cement, fracture and fatigue resistance appeared to be independent of sterilization method. This independence is believed to be the result of higher porosity that compromised the mechanical properties and obscures any effect of sterilization. Our results indicate that a combination of nonionizing sterilization and vacuum mixing resulted in the best mechanical performance and is most likely to contribute to enhanced longevity in vivo.

Toughening of layered ceramic composites with residual surface compression: effects of layer thickness

Shielding of edge cracks in multilayer single-edge-notch-bend (SENB) specimens, with alternating layers designed to produce residual compression and balancing tension, was calculated by the method of weight function. Investigation of the effects of the relative thickness of the layers and of the number of layers revealed that the maximum crack shielding and the maximum apparent fracture toughness were achieved in three-layer composites with the thickness of the compression layer constituting one-half of the specimen height with an edge crack extending to the first interface. These theoretical predictions were confirmed with measurements of apparent fracture toughness in the range, 28–32 MPa√m, on three-layer SENB specimens of alumina–zirconia composites.

Effects Of Aging On Fracture Behavior OfPolycarbonate

Polycarbonate (PC) is one of the toughest, most versatile engineering thermoplastics. However, due to physical aging phenomenon, the polymer can break in a brittle manner at normal temperature with relatively low loading rates. The aim of this work is to study the effects of aging on the brittle-ductile transition temperature (7) and the yielding behavior of an unmodified PC. Fractures tests were performed over a range of loading rates from 0.2mm/min to 2.5 m/s, using the single edge notched bending specimen (SENB). 7 was determined from the observed fracture behavior as a function of loading rate and temperature. Their relationship is analysed by an activation energy approach, using the Arrhenius-type equation. The results show that ageing increases the temperature at brittle-ductile transition of the polymer and this effect is more important at high loading rates. The activation energy seems to change with temperature, suggesting that the time-temperature dependence of the brittleductile transition is not controlled by a single molecular relaxation process. Plane strain compression tests were carried out over a range of strain-rates from 0.001 to 0.5 s and a range of temperatures from -80 to 60°C for samples annealed from 12 to 240 hours. The Ree-Eyring model is used to determine the energy activation energies of the primary and secondary molecular relaxation processes, and to analyse the correlation between strain rate and temperature. This model supplies an acceptable fit to the experiment data for analysing timeaging-temperature dependence of yielding. Damage & Fracture Mechanics VI, C.A. Brebbia, A.P.S. Selvadurai, (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-812-0

Notch effect of surface compression and the toughening of graded Al 2O 3/TiC/Ni materials

The fracture behavior of graded Al 2O 3/TiC/Ni materials with a symmetric structure was investigated using single-edge notch-bend (SENB) specimens with surface compression. The fracture toughness of the graded materials was determined according to ASTM Standard E399. The results show that the effective fracture toughness increases with an increase in notch depth in the compressive stress zone, and reaches the maximum of 39.2 MPa m 1/2 at the interface of compressive/tensile stress zones. Finite element analysis reveals that the surface compression will be intensified at the notch root once the specimen is edge-notched because of the stress concentration, and the degree of the compressive stress intensification increases with an increase in notch depth. The dependence of the effective fracture toughness of the graded materials on the notch depth shows a behavior similar to the R-curve that is usually associated with microstructural toughening mechanisms. This toughening behavior is caused by the intensification of the compressive stress concentration with the increase of the notch depth. A theoretical analysis based on fracture mechanics verifies that the mechanical reliability of brittle ceramics can be improved effectively by tailoring and controlling the internal stresses.

Identification of Gurson-Tvergaard material model parameters via Kalman filtering technique. I. Theory

In this paper quasi-static ductile fracture processes are simulated within the framework of the finite element method by means of the Gurson–Tvergaard isotropic constitutive model for progressively cavitating elastoplastic solids. The progressive degradation of the material strength properties in the fracture process zone due to micro-void growth to coalescence is modeled through the computational cell concept. Among the several model parameters to be calibrated in the computations, attention is restricted to the Tvergaard coefficients q1 and q2 and to the initial porosity f0 in the unstressed configuration. To identify these model parameters the inverse problem is solved via the extended Kalman filter for nonlinear systems coupled to a numerical methodology for the sensitivity analysis. In part I of this work the theory of Kalman filtering and sensitivity analysis is presented. First results concerning the identification of the Tvergaard parameters for a whole crack growth in single edge notched bend specimens made of a pressure vessel steel are presented. In order to enhance the convergence towards the final solution of the identification procedure, during the tests measurements are made of the displacements of points located in the central portion of the notched specimens, where model parameters highly affect the system state variables. In part II of this work a numerical validation of the proposed procedure in terms of uniqueness of the final identified solution, requirements of accuracy for the Bayesian initialization of the model parameters and sensitivity to the experimental measurement errors will be presented and discussed.

Analysis of the geometry dependence of fracture toughness at cracking initiation by comparison of circumferentially cracked round bars and SENB tests on Copper

In the first part of the paper, the use of circumferentially cracked round bars (CRB geometry) for characterizing fracture toughness of a ductile material, namely copper, is assessed experimentally through a comparison with the single edge notched bend (SENB) geometry. The J(R) curve method with multiple-specimens was applied, but, as unstable cracking appeared very early in the CRB specimen, an engineering definition of fracture toughness was not pertinent. Unloaded specimens were analyzed metallographically to determine the CTOD at physical cracking initiation. The fracture toughness measured using the CRB geometry was 50% larger than using the SENB geometry. The second part of the paper aims at justifying this difference of fracture toughness at cracking initiation. Finite element simulations revealed a slightly higher constraint in the SENB specimens. The main difference between the two specimen geometries lies in a 50% larger extension of the finite strain zone with respect to the CTOD in the case of the SENB specimens. Based on the observation that, in the studied material, the critical CTOD is one order of magnitude larger than the void spacing, we conclude that the geometry dependence of the fracture toughness is caused by the difference in the finite strain zone extension rather than by a stress triaxiality effect.

Mechanical properties of new composite restorative materials.

Determination of flexural strength, flexural modulus, fracture toughness, Vickers hardness, and wear resistance of condensable composites (Solitaire, Surefil, Alert) and an ormocer (Definite) in comparison with a hybrid composite (Tetric Ceram) and an ion-releasing composite (Ariston pHc). Flexural strength, flexural modulus, and fracture toughness were determined in 3-point bending. Single-edge notched-bend specimens were used to evaluate fracture toughness. Microhardness was measured with a Vickers indenter. Wear was determined in a pin-on-block-design with a Degusit antagonist at 50 N load and quantified by a replica technique after 6000, 10000, 30000, and 50000 load cycles using a 3D-laser scanner. All results were statistically analyzed with ANOVA and post hoc Tukey HSD tests. Alert exhibited the highest flexural modulus, K(IC), and hardness, but lowest wear resistance. Solitaire presented the highest wear resistance, but significantly lower flexural strength, flexural modulus, K(IC), and hardness than all other materials. No significant correlation could be detected between hardness and wear of the tested composites with Pearson's correlation coefficient. The condensable composites differed significantly in their mechanical properties. This study suggested that, besides the filler content level and filler size, other factors like matrix-filler interactions highly influence the fracture and wear behavior of the materials.

Mechanical properties and wear behavior of light-cured packable composite resins

Objectives: Determination of flexural strength, flexural modulus, fracture toughness and wear resistance of three packable composites (Solitaire, Surefil, ALERT) and a packable ormocer (Definite) in comparison with an advanced hybrid composite (Tetric Ceram) and an ion-releasing composite (Ariston pHc). Methods: Flexural strength, flexural modulus and fracture toughness of each material were determined in three-point bending (each test n=10). Single-edge notched-bend specimens were used to evaluate the fracture toughness ( K IC). Wear of the materials ( n=8) was determined in a pin-on-block-design with a spherical Degusit antagonist at 50 N vertical load and quantified by a replica technique using a 3D-laser scanner. Replicas were made after 6000, 10000, 30000 and 50000 load cycles. The mean wear rate (MWR (μm 3 cycle −1)) was obtained by a linear regression analysis in the steady-state of the time–wear-curve. All results were statistically analyzed with ANOVA and post hoc Tukey HSD tests ( p<0.05). Results: ALERT exhibited the highest flexural modulus (12.5±2.1 GPa) and K IC (2.3±0.2 MN m −3/2), but the lowest wear resistance (8275 μm 3 cycle −1). Solitaire presented the highest wear resistance (1591 μm 3 cycle −1), but significantly lower flexural strength (81.6±10.0 MPa), flexural modulus (4.4±0.3 GPa), and K IC (1.4±0.2 MN m −3/2) than all other materials. Surefil revealed a significantly higher flexural modulus (9.3±0.9 GPa) and wear resistance (3028 μm 3 cycle −1) than Tetric Ceram (6.8±0.5 GPa; 5417 μm 3 cycle −1) and Ariston pHc (7.3±0.8 GPa; 7194 μm 3 cycle −1). Significance: The tested packable composite resins differed significantly in their mechanical properties. This study suggested that fracture and wear behavior of the composite resins are highly influenced by the filler system. Overall, Surefil demonstrated good fracture mechanics parameters and a low wear rate.

On Higher-Order Crack-Tip Fields in Creeping Solids

In view of the near-tip constraint effect imposed by the geometry and loading configuration, a creep fracture analysis based on C* only is generally not sufficient. This paper presents a formulation of higher-order crack-tip fields in steady power-law creeping solids which can be derived from an asymptotic development of near-tip fields analogous to that of Sharma and Aravas and Yang et al. for elastoplastic bodies. The higher-order fields are controlled by a parameter named A2*, similar as in elastoplasticity, and a second loading parameter, σ∞. By means of the scaling properties for power-law materials, it is shown that A2* for a flat test specimen is independent of the loading level. Finally, we carry out small-strain finite element analyses of creep in single-edge notched tension, centered crack panel under tension, and single-edge notched bending specimens in order to determine the corresponding values of A2* for mode I cracks under plane-strain conditions. [S0021-8936(00)01202-2]