Double Edge Notch Research Articles

Effect of Stress Concentration on Tensile Fracture Behavior of Carbon-Carbon Composites

The effect of stress concentrations on tensile fracture behavior of carbon-carbon (C/C) composites was investigated using circularly holed specimens and double-edge-notched (DEN) specimens. As for the circularly holed specimens, the tensile fracture stress was much higher than that estimated from the maximum stress criterion, which suggest that major stress relaxation mechanisms should exist. On the other hand, the linear elastic fracture mechanics can be applied to the DEN specimen, which means the damaged zone should be small enough compared with the notch length. In order to discuss the magnitude of the stress relaxation, damaged regions of the two kinds of testing geometry were estimated using the point stress criterion. The estimation led to remarkable difference in the size of the damaged regions, which will explain the difference in the magnitude of the stress relaxation. Through the observations of fractured specimen, it was deduced that not only the shear deformation but delamination along fiber bundles and opening of transverse crack would relax the stress concentrations. The other mechanism was also proposed based on the testing results, that is strength increase in the damaged region.

Some applications of two-dimensional stress transfer analyses

Two-dimensional stress transfer analyses are performed for the following system: a long central plate bonded on opposite sides along its length to two short plates and subjected to tensile loading at its ends. The load transfers from the long plate to the short plate through the interfacial shear stress. The system represents the unit cell of platelet-reinforced composites, in which parallel matrix cracks are uniformly spaced and are bridged by the platelet, in a two-dimensional sense. Analytical solutions for the crack opening displacement, the additional displacement of the composite due to the presence of cracks, and stress intensity factor at the crack tip are derived. Letting the long plate and the short plates have the same mechanical properties, the analytical solutions are compared to the existing numerical solutions for tensile loading of both a double edge notch strip and a semi-infinite plane with parallel edge cracks. Good agreement is obtained in this comparison.

Dependence of Intralaminar Fracture Toughness on Direction of Crack Propagation in Unidirectional Composites

Mode I intralaminar fracture toughness GIC of graphite fiber-reinforced bismaleimide (X5260/G40-800) has been studied experimentally using double edge notch (DEN) specimens and three-point-bend specimens. The intralaminar fracture toughness was found to depend significantly on the direction of fracture propagation. Examination of the fracture surface showed the fracture surface to be relatively smooth or ragged depending on the direction of the fracture propagation, thus substantiating the measured differences in of graphite fiber-reinforced bismaleimide (X5260/G40-800) has been studied experimentally using double edge notch (DEN) specimens and three-point-bend specimens. The intralaminar fracture toughness was found to depend significantly on the direction of fracture propagation. Examination of the fracture surface showed the fracture surface to be relatively smooth or ragged depending on the direction of the fracture propagation, thus substantiating the measured differences in GIC. Furthermore the material exhibited a substantial. Furthermore the material exhibited a substantial R-curve behavior, which appeared related to fiber pull-out.

Fracture Behaviour of Chopped Glass Strand Reinforced Phenolic Composites

Modified phenolic composites were fabricated by compression moulding a mixture of chopped glass strands and a cashew nut shell liquid modified phenolic resin. Single edge notched bend (SENB) tests, double edge notched (DEN) tension tests and 3-point flexure tests on unnotched specimens were conducted at various fibre volume fractions and strand lengths. The candidate stress intensity factors of SENB specimens were significantly higher than those of DEN specimens. Glass strand/phenolic interface debonding and strand pull-out were observed for both SENB and DEN specimens. In addition, the DEN specimens exhibited a considerable degree of splitting of glass strands parallel to their axes. By increasing the fibre volume fraction and the strand length, it was possible to improve the flexural strength without adversely affecting the fracture toughness.

Fracture Behaviour of Chopped Glass Strand Reinforced Phenolic Composites

Modified phenolic composites were fabricated by compression moulding a mixture of chopped glass strands and a cashew nut shell liquid modified phenolic resin. Single edge notched bend (SENB) tests, double edge notched (DEN) tension tests and 3-point flexure tests on unnotched specimens were conducted at various fibre volume fractions and strand lengths. The candidate stress intensity factors of SENB specimens were significantly higher than those of DEN specimens. Glass strand/phenolic interface debonding and strand pull-out were observed for both SENB and DEN specimens. In addition, the DEN specimens exhibited a considerable degree of splitting of glass strands parallel to their axes. By increasing the fibre volume fraction and the strand length, it was possible to improve the flexural strength without adversely affecting the fracture toughness.

The Influence of Loading Rate on the Mode II Interlaminar Fracture Toughness of Composite Materials

The effect of varying loading rate on the mode II interlaminar fracture toughness of a range of composite materials has been investigated. A screw-driven universal testing machine and a fully instrumented drop-weight carriage have been used to obtain crosshead speeds in the range 0.01 mm/min to 3 m/s. The results have shown that the value of GIIc for many composites is rate-sensitive, tending to increase with increasing loading rate. Damage development in the crack tip region has been investigated by examining the polished edges of a number of test specimens in a scanning electron microscope. It has also been shown that offsetting the center plies by a few degrees in order to reduce fiber bridging results in a greater degree of rate-sensitivity in GIIc. It is believed that the presence of fiber-bridging in standard unidirectional fracture-mechanics samples conceals much of the intrinsic viscoelastic response of the polymeric matrix. Failure mechanisms at the crack tip have been investigated using the Double Edge Notch Flexure specimen. A scanning electron microscope study of this region has shown that the size and nature of this zone is dependent upon the crosshead displacement rate.

Crack growth response of IMI 834 under variable amplitude loading

The paper addresses the application of constant load amplitude fatigue crack growth data in the prediction of crack development at stress concentrations subjected to variable amplitude loading. The variable amplitude cycles were applied in repeated blocks. Several loading forms were evaluated in which each block included a single major cycle and either 5, 20 or 100 minor cycles with amplitudes between 30 and 70% that for the major cycle. The relative position of the minor cycle is also varied. The basic behaviour of the IMI 834 alloy was measured on corner crack specimens at R values of 0, 0.3, 0.5 and 0.7. It is shown that the resultant growth rate response can be correlated either by the Walker relationship or by a closure correction approach. Closure values for the latter were measured by a D.C. potential drop monitoring system and illustrate a similar dependence on load ratio, R, as reported by Elber (with U = 0.72 + 0.1 R + 0.45 R 2). The closure corrected growth rate data follow a power law relationship but display two regimes of behaviour with an exponent of 1.9 at low stress intensity factors and 3.6 above a transition point. The closure corrected growth rates are used in a numerical model to predict crack development within two notch geometries. For a double edge notch configuration, ‘ a against N’ response is predicted to a high level of accuracy for several distinct major/minor cyclic combinations. However, discrepancies are observed for a more highly stressed cylindrical notch specimen. These are attributed to geometry induced closure. and interactions from overload/underload excursions.

走査型電子顕微鏡内クリープ疲労試験による切欠き材の微視的損傷過程

In order to evaluate the crack initiation life precisely in the stress concentration portion of high-temperature components in power plants, it is important to comprehend the microscopic damage process under localized stress distribution. In this study, fatigue and creep-fatigue tests with tensile hold time were conducted on SUS304 stainless steel specimens, having V shaped double-edge notch, by using a high-temperature fatigue testing machine combined with a scanning electron microscope (SEM). As the results, it was found that the microscopic damage under the fatigue condition progressed by the initiation and propagation of a single main crack due to the accumulation of slip bands caused by strain concentration in the limited region around the notch root. On the other hand, under the creep-fatigue condition, many microcracks initiated in grain boundaries around the root corresponding to the microstrain distribution with a smooth gradient from the notch root. The main crack at the root was formed by coalescence of those microcracks and propagated by coalesing with the microcracks distributing ahead of the microcrack.

Size Effect and Fracture Characteristics of Composite Laminates

Measurements of the size effect on the nominal strength of notched specimens of fiber composite laminates are reported. Tests were conducted on graphite/epoxy crossply and quasi-isotropic laminates. The specimens were rectangular strips of widths 6.4, 12.7, 25.4 and 50.8 mm (0.25, 0.50, 1.00 and 2.00 in.) geometrically similar in two dimensions. The gage lengths were 25, 51, 102 and 203 mm (1.0, 2.0, 4.0 and 8.0 in.). One set of specimens had double-edge notches and a [0/922]s crossply layup, and another set had a single-sided edge notch and a [0/±45/90]s, quasi-isotropic layup. It has been found that there is a significant size effect on the nominal strength. It approximately agrees with the size effect law proposed by Bazˇant, according to which the curve of the logarithm of the nominal strength versus the logarithm of size represents a smooth transition from a horizontal asymptote, corresponding to the strength criterion (plastic limit analysis), to an inclined asymptote of −0.5 slope, corresponding to linear elastic fracture mechanics. Optimum fits of the test results by the size effect law are obtained, and the size effect law parameters are then used to identify the material fracture characteristics, particularly the fracture energy and the effective length of the fracture process zone. Finally, the R-curves are also identified on the basis of the maximum load data. The results show that in design situations with notches or large initial traction-free cracks the size effect on the nominal strength of fiber composite laminates must be taken into account.

Experimental and numerical investigation of fracture in double-edge notched steel plates

Double-edge notched (DENT) steel plates were pulled until complete fracture and several experimental observations were made (using profilometry and scanning electron microscopy). The essential work of fracture (EWF) model was found to be well verified. Numerical simulations - up to the maximum load only - of some experiments were performed using the finite element method (FEM), and incorporating geometric and material non-linearities (large deformation elasto-plasticity). Some experimental measurements were compared with the corresponding numerical computations and excellent agreement was found.

A JD expression for the double edge notch tension configuration

The paper derives an expression for the plastic component, JDP, of the deformation J integral, JD, for the double edge notch tension configuration. JDP is expressed in terms of the energy and complementary energy integrals via eta factors, whose values are obtained by ensuring that JDP assumes the correct form at the two extreme levels of deformation: extensive deformation at limit load conditions and small-scale yielding. The expression gives a greater JDP value than that given by the expression which is obtained by assuming that the remaining ligament width is small compared with the specimen width; this latter expression is sometimes used when determining a JDP crack growth resistance curve using a double edge notch tension specimen.

Stress intensity factors for V-notched strip under tension or in-plane bending

The singular stress field around a sharp notch tip is expressed as a sum of two independent fields: a symmetric field with a stress singularity % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaac+% cacaWGYbWaaWbaaSqabeaacaaIXaGaeyOeI0Iaeq4UdW2aaSbaaWqa% aiaaigdaaeqaaaaaaaa!3CC3!\[1/r^{1 - \lambda _1 } \]and a skew-symmetric field with a stress singularity % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaac+% cacaWGYbWaaWbaaSqabeaacaaIXaGaeyOeI0Iaeq4UdW2aaSbaaWqa% aiaaikdaaeqaaaaaaaa!3CC4!\[1/r^{1 - \lambda _2 } \]. The intensities of the symmetric and skew-symmetric singular stress fields are defined in terms of constants KI and KII, respectively. In this study, a plane problem of a strip with single or double edge notches under tension or in-plane bending is considered. The bisector of the notch may be inclined to the edge, so that the two singular stress fields with different singularities may be created simultaneously at the notch tip. The body force method is used to calculate the stress intensity factors KI and KII. In numerical analysis, basic density functions of the body forces are introduced to characterize the stress singularity at the notch tip. The advantages of this technique are the high accuracy of results, due to the smoothness of the unknown weight functions, and the presence of the direct relation between the values of KI and KII and the values of unknown weight functions. The stress intensity factors are systematically calculated for the various geometrical conditions.

Finite element validation of stress intensity factor calculation models for thru-thickness and thumb-nail cracks in double edge notch specimens

Stress intensity factors for thru-thickness and thumb-nail cracks in the double edge notch specimens, containing two different notch radius (R) to specimen width (W) ratios (R/W = 18 and 116), are calculated through finite element analysis. The finite element results are compared with predictions based on existing empirical models for SIF calculations. The effects of a change in R/W ratio on SIF of thru-thickness and thumb-nail cracks are also discussed.

A novel method for measuring plane stress dynamic fracture toughness

By using the self-designed Rotating Circular Disk direct tensile impact apparatus, a novel test method has been developed for studying the fracture properties of materials under impact loading. A double edge notch specimen under a plane stress state is used in fracture test conditions; the material exhibits elastic-plastic behavior at the crack tip. The SHPB technique is used to measure the dynamic loads and the displacements of the specimen; crack opening displacement is measured by applying the self-designed photoelectric transformation setup. For the evaluation of dynamic fracture toughness, the extended J-integral with the inertial effect is calculated by Rice's formula using the average load-displacement curve. The time to crack initiation is determined by the compliance changing rate method. The fracture toughness of LY12cz aluminum alloy at a loading rate K ID greater than 10 6 MPa √m/sec is obtained.

Predicting crack arrest in a pure tensile loading configuration

Analysis of the double-edge notch configuration, where the remaining ligament is subjected to pure tensile loading, shows that the ratio of the reflectionless stress intensity factor K∗ I to the linear elastic stress intensity factor K ST I is appreciably higher than it is for the case where a ligament is subjected to bend loading. The implication is that the ASME Code crack arrest procedure, which is based on K ST I , provides a more accurate arrest prediction for tensile loading than it does for bend loading.

Effect of mechanical heterogeneity on the behavior of a crack in the weld heat affected zone: A numerical analysis

Both mechanical heterogeneity and crack position effects on the stress and strain fields at the crack tip of overmatching and undermatching weld metal joints are investigated. Analyses under sustained plane strain yielding conditions of a notch “near to” and “at” the interface between two elastic-plastic materials of a double edge notch tensile specimen have been carried out by finite element method. The results are used to study the implications of the difference in plastic properties on the behavior of a crack in the weld heated affected zone (HAZ), as well as to discuss its more critical position, regarding the fusion line, for the evaluation of HAZ weld fracture toughness. The contribution to the notch tip opening displacement of each material in heterogeneous cases, and the notch tip sliding displacement, have been related to remote load for the different cases considered.

Finite element modeling of the time‐dependent behavior of nonlinear ductile polymers

AbstractA finite element algorithm developed previously has been successfully extended to the study of nonlinear time‐dependent problems. Nonlinear viscoelastic and viscoplastic models have been used to study the time‐dependent deformation and failure of high density polyethylene (HDPE). Two classes of nonlinear models have been identified; those that allow stress redistribution with time under specified traction boundary conditions, and those that do not. The implications of using viscoelastic vs. viscoplastic models, as well as the specific mathematical form of the constitutive equations selected for use, have been studied. Strains predicted using the FE algorithm have been compared with experimental measurements for (i) a HDPE plate with a hole and (ii) a double edge notch HDPE specimen, both under remote tension. Excellent agreement was obtained between numerical predictions and the experimental values.

Crack propagation behavior under creep conditions

The creep crack propagation behavior of a Cr−Mo−V rotor steel has been investigated at 538°C using time-dependent fracture mechanics concepts. The creep crack propagation lives and the creep deflection rates of double-edge-notched (DEN) specimens were estimated using previous data from compact-type specimens. The predicted crack growth lives and deflection rates compared favorably with the experimental data. When plotted as a function of the C t parameter, the experimentally determined creep crack propagation rates of DEN specimens were found to be in agreement with those of compact and center-crack-tension specimens. These results provide further experimental verification for the validity of the C t parameter for characterizing creep crack growth behavior. Some discrepancies between the predicted and the observed behavior are attributed to primary creep deformation behavior which was not considered in estimating the value of C t .

Corrosion and compatibility: Berry, W.E. CAB Curr. Aware. Bull. (194), 6 Oct. 1989

Compact, C(T), specimens are commonly used for fatigue and creep-fatigue crack growth testing under constant-load-amplitude conditions. The use of the standard C(T) specimens [ASTM] is limited to positive load ratios. They are also limited in the amount of crack growth data that can be developed at high stress intensity values due to accumulation of plastic and/or creep strains leading to ratcheting in the specimen. Testing under displacement control can potentially address these shortcomings of the load-controlled tests for which the C(T) geometry is unsuitable. A double edge notch tension–compression, DEN(T–C), specimen to perform displacement controlled creep-fatigue crack growth testing is developed and optimized with the help of finite element and boundary element analyses. The specimen has threaded cylindrical ends for applying the loads. The test section is rectangular with a half width, W, and half height, H, and a constant thickness, B. The height to width ratio, H/W, of the specimen must be kept low to avoid buckling during compressive loading while ensuring that the stress-intensity parameter values are not strongly dependent on the chosen H/W value. Simple optimization analysis shows that a H/W ratio of 1.2 is likely to best meet these requirements. However, only performing actual experiments will confirm whether this choice of H/W value is optimum.In the finite element analyses, the specimen is modeled using an effective height (heff) to width (W) ratio, heff/W, of 1.46 to account for the fillet regions on the two ends of the specimens. Accurate expressions for estimating the fracture mechanics crack tip parameters such as the stress intensity parameter, K, the crack mouth opening displacement (CMOD), and the load-line displacement (LLD) are developed over a wide range of crack sizes for the DEN(T–C) specimen. Expressions are also developed for crack size as a function of specimen compliance.

Fracture Behaviour of Carbon/Epoxy Composites with Damage Consideration

This paper presents an investigation of the effects of test specimen geometries and load ing conditions of different stacking sequences on the fracture behaviour of carbon/epoxy laminates with damage consideration. The specimen geometries chosen are single edge notched (SEN), double edge notched (DEN), centre notched (CN), three point bending (TPB) and compact tension (CT) specimen while the stacking sequences are [0] s, [0/90] s, [03/902]s, [90/0/±45]s, [±45], and [90]s. The development of damage within the test pieces were monitored using acoustic emission, COD measurement, optical microscopy and scanning electron microscopy (SEM). These experimental methods are shown to be capable of assessing the development of damage and characterizing fracture behaviour of carbon/epoxy composites under consideration.