Single-edge Bend Research Articles

A Numerical Study on Effective Modulus of Elasticity in Crack Length Evaluation for Single-Edge Bending Specimens

Abstract The actual state of stress in the remaining ligament of a single-edge bending (SE(B)) specimen, which is neither plane stress nor plane strain, is critical in accurately predicting the crack length in the specimen involved in the unloading compliance method. Three-dimensional finite element analyses were carried out in this study to evaluate the effective modulus of elasticity that reflects the actual state of stress corresponding to the crack mouth opening displacement (CMOD) compliance of the SE(B) specimen. Both plane-sided and side-grooved specimens with a wide range of geometric configurations and crack lengths were included in the study. A practical approach is further proposed to quickly evaluate the effective modulus from the CMOD compliance determined based on the test data. The proposed approach was verified using experimental data and numerical analysis results. The results of the verification suggest that replacing the elastic modulus corresponding to the plane stress or plane strain condition with the effective modulus in commonly used a/W–CMOD compliance equations can markedly improve the accuracy of the predicted crack length.

A Study on the Fitting Accuracy of CMOD Compliance Equations

Abstract The maximum error of the inverse fitting of Tada et al.’s equation of the a/W–crack mouth opening displacement (CMOD) compliance equation proposed by Joyce and adopted in ASTM E1820-11 for single edge bend [SE(B)] specimens with shallow cracks (0.05 ≤ a/W < 0.45) is observed to be 2.03 % for 0.05 < a/W < 0.1. A new a/W–CMOD compliance equation with the same fifth-order polynomial fitting applicable for SE(B) specimens with 0.05 ≤ a/W ≤ 0.7 is therefore proposed. The maximum fitting error of the proposed equation is approximately 0.19 %.

Improved Incremental J-Integral Equations for Determining Crack Growth Resistance Curves

The J-integral resistance curve is the most important material properties in fracture mechanics that is often used for structural integrity assessment. ASTM E1820 is a commonly accepted fracture toughness test standard for measuring the critical value of J-integral at the onset of ductile fracture and J-R curve during ductile crack tearing. The recommended test procedure is the elastic unloading compliance method. For a stationary crack, the J-integral is simply calculated from the area under the load-displacement record using the η-factor equation. For a growing crack, the J-integral is calculated using the incremental equation proposed by Ernst et al. (1981, “Estimations on J-integral and Tearing Modulus T From a Single Specimen Test Record,” Fracture Mechanics: Thirteenth Conference, ASTM STP 743, pp. 476–502) to consider the crack growth correction. For the purpose of obtaining accurate J-integral values, ASTM E1820 requires small and uniform crack growth increments in a J-R curve test. In order to allow larger crack growth increments in an unloading compliance test, an improved J-integral estimation is needed. Based on the numerical integration techniques of forward rectangular, backward rectangular, and trapezoidal rules, three incremental J-integral equations are developed. It demonstrates that the current ASTM E1820 procedure is similar to the forward rectangular result, and the existing Garwood equation is similar to the backward rectangular result. The trapezoidal result has a higher accuracy than the other two, and thus it is proposed as a new formula to increase the accuracy of a J-R curve when a larger crack growth increment is used in testing. An analytic approach is then developed and used to evaluate the accuracy of the proposed incremental equations using single-edge bending and compact tension specimens for different hardening materials. It is followed by an experimental evaluation using actual fracture test data for HY80 steel. The results show that the proposed incremental J-integral equations can obtain much improved results of J-R curves for larger crack growth increments and are more accurate than the present ASTM E1820 equation.

Exploring the reduction of laboratory testing for the cohesive zone model for asphalt concrete

The cohesive zone model is a popular tool used to predict cracking in asphalt concrete. However, two of the three inputs required for the cohesive zone model, tensile stress and fracture energy, come from destructive laboratory tests. If the peak load from a fracture test (which supplies fracture energy) could be substituted for the tensile strength, the amount of laboratory testing could be halved. This research compared the peak loads from the single-edge notch beam, semi-circular bend and disk-shaped compact tension fracture tests as well as the tensile strength from the standard indirect tension (IDT) test. Even accounting for specimen geometry, the data did not indicate consistent correlation of the three fracture tests with the IDT test across various testing temperatures, loading rates or sample type (laboratory vs field samples). Therefore, no fracture test provided a sufficiently robust correlation to recommend replacing the tensile strength with the peak load of the fracture test for the cohesive zone model.

Effect of residual stresses on crack behaviour in single edge bending specimens

ABSTRACTResidual stresses due to manufacturing processes, such as welding, change the load bearing capacity of cracked components. The effects of residual stresses on crack behaviour in single edge bending specimens were investigated using Finite element analyses. Three parameters (J, Q and R) were used to study the crack behaviour. The J‐integral predicts the size scale over which large stresses and strains exist, the constraint parameter Q describes the crack‐tip constraint as a result of geometry, loading mode and crack depth and the constraint parameter R is used to describe the constraint resulting from residual stresses. To carry out a systematic investigation on the effect of residual stresses on the J‐integral and crack‐tip constraints, models under different combinations of residual stresses and external loads with different crack depths were analysed. It has been shown that the crack‐tip constraint R increased by tensile residual stresses around the crack‐tip. On the other hand, the constraint parameter R decreased and tended to zero at high external load levels.

Scatter band prediction for fracture toughness of specimens with prior load

This study investigates the warm pre-stress effects under Load–Unload–Cool–Fracture transient with deep-cracked single edge bend specimens of a high strength steel. In the experiment, it has been found that warm pre-stressing increases the apparent overall elastic–plastic fracture toughness KJc_total compared to those of as-received specimens. A simple prediction procedure for fracture toughness of specimens with warm pre-stressing is proposed based on critical plastic zone criterion using fracture parameter superposition rule. It is shown that the increase and the narrower scatter band of fracture toughness of specimens with prior load can be well evaluated within the framework of the Master Curve methodology.

Ductile extension of 3-D external circumferential cracks in pipe structures

This study investigates the ductile fracture resistance of 3-D external circumferential cracks in the wall of a steel pipe under remote tension, using a damagemechanism model originally proposed by Gurson and Tvergaard. The ductile crack extension utilizes an element extinction technique implemented in the computational cell framework. The key parameter for the computational cell method, i.e., the initial porosity ratio f0, is calibrated using both the fracture resistance and the load-deformation responses obtained from fracture tests of multiple single-edge bend [SE(B)] specimens made of high-strength steel, HY80, which has a yield strength of 630 MPa. The fracture resistance along the 3-D semi-elliptical crack front is computed from the calibrated cell model. Based on the similarity concept in the near-tip stress-strain fields, this study demonstrates that an equivalent 2-D axi-symmetric model provides conservative estimations of the fracture resistance for 3-D circumferential cracks in pipes.

Multiscale fatigue crack observations on Ti–6Al–4V

The fatigue process of dynamic loaded materials can generally be classified in four stages, namely crack initiation, short crack growth, long crack growth and rupture. A continuous fracture mechanical description of the crack growth stages under consideration of the crack initiation phase was the aim of this research. The fatigue behavior of forged Ti–6Al–4V with three different microstructures were thereby characterized on the basis of multiscale fatigue crack observations on electrolytically polished hourglass specimens loaded in the finite life region. The gathered crack propagation data was compared with single-edge bending long crack growth curves. It was determined that the crack initiation phase accounts for less than 5% of the total lifetime. Depending on the (α + β)-content, the fatigue behavior is dominated either by primary α-grain size (equiaxed-type microstructures) or colony length of the (α + β)-lamellae (bimodal-type microstructures). Transcrystalline crack propagation was observed for all microstructures. The comparison of the multiscale fatigue crack growth rates with single-edge bending long crack growth curves revealed that the short crack growth behavior is the extension of the Paris-region of the long crack growth curve, and can be fitted with a power law for lifetime estimation.

The Mechanics Behavior Tests of HPS-485W Made in China

This paper gives a brief introduction of the developmental history of high performance steel (HPS) all over the world. Emphasis of current paper is on the characteristic studies of HPS 485W, which is new structural weathered steel produced by Wuyang Steel Iron Company using quenching and tempering (Q&T) in China. To obtain the strength and ductility of HPS 485W, the tensile coupons were machined from each 8mm, 10mm, 12mm and 14mm thick plate. Based on the static tensile tests in room temperature, major of material mechanical characters were obtained, such as yield strength, ultimate strength, elastic modulus and so forth. Besides, to examine plate toughness, 30 Charpy V-Notch (CVN) specimens from 12mm thick HPS 485W plate were tested from 20 oC to -196 oC . Compared with conventional bridge steels, the CVN test results show that the fracture toughness of HPS 485W is much higher, and the brittle-ductile transition of HPS occurs at a much lower temperature. A set of 9 single-edge bend specimens were took from 20mm and 30mm thick HPS 485W separately for ductility fracture toughness test. The calculated JIC value is 415.8 kJ/m2 for 18mm thick specimen and 507.79 kJ/m2 for 28mm thick specimen, which shows ideal ductility of HPS 485W.

Large scale testing and statistical analysis of dynamic fracture toughness of ductile cast iron

The present paper deals with the experimental determination and statistical analysis of dynamic fracture toughness values of ductile cast iron. K Id data from 140 mm thick single edge bend specimens of two dynamic fracture toughness test series on ductile cast iron from heavy-walled castings were analysed. At first, the statistical analysis of data at −40 °C was done based on ASME Code Case N-670 using a two-parameter Weibull distribution function. Weibull analyses of three samples covering different pearlite contents (⩽4%, ⩽9%, ⩽20%) were performed and characteristics of the distribution functions as well as two-sided confidence intervals were calculated. The calculated characteristics show that K Id of ductile cast iron decreases with increasing pearlite content. In a second step, the applicability of the Master curve procedure according to ASTM E 1921 to ductile cast iron materials was investigated and it was formally used for statistical analysis of ductile cast iron dynamic fracture toughness data. Although the Master curve method was originally introduced for static fracture toughness data of ferritic steels, the successful individual analyses performed here support the engineering way taken to apply the method to ductile cast iron materials too. The results of both methods, the Master curve procedure and the ASME Code Case N-670, show acceptable congruity. At the same time, it is concluded from the present study that further investigations and experiments are required to improve precision and for verification before the results could be applied within component safety analyses.

On Fracture Mechanics Testing Technique Based on Compliance of Specimens

Based on compliance testing of a straight-notch compact tensile (SN-CT) or a single edge bending (SEB) specimen, this paper present a formula with increment form to calculate plastic part of J-integral, two formulas for a SN-CT specimen and a SEB specimen to transform crack mouth opening displacement (CMOD) v0 to the crack opening displacement (COD) q along load line, and simplified formulas to estimate crack length a and effective young’s modulus E. Furthermore, the relation between v and q of the SN-CT specimens of 45 steel and SEB specimens of 30Cr steel were investigated. The results show that the formulas to describe the relation between the ratio v/q and the dimensionless crack length a/w of the specimens accord with the testing results better.

Simulation of ballistic impact tests under various conditions for a nickel-base superalloy

Smooth and round notched tensile specimens with three different notch radii as well as single-edge bending specimens were tested in two high strain-rate testing machines at various strain-rates and temperatures. The experimental data were used to identify the parameters of the Johnson-Cook deformation and failure model using the evolution strategy and LS-DYNA calculations respectively. Ballistic tests with both, the projectiles and target plates made from the same material were performed at different projectile velocities and with two different projectile tip shapes (blunt and conical) as well as with three different target thicknesses, target angles and at two different target temperatures. The calibrated Johnson-Cook models were successfully applied in LS-DYNA in an uncoupled manner to simulate these tests. In all FE simulations the integrative nonlocal Pijaudier-Cabot & Bazant method was applied for reducing the mesh dependency of the failure time.

Fracture toughness characterisation in the ductile-to-brittle transition and upper shelf regimes using pre-cracked Charpy single-edge bend specimens

Fracture toughness data of pre-cracked Charpy single-edge bend, SE(B), specimens are compared with those of standard compact, C(T), specimens in the upper shelf and ductile-to-brittle transition regimes. Charpy sized SE(B) specimens provide ductile fracture toughness data, which are compatible with those of standard C(T) specimens. Statistical methods such as the exponential curve fitting method (ECF), the engineering lower bound toughness method (ELB), and the Master Curve method (MC) are used to provide meaningful lower bound cleavage fracture toughness estimates from the toughness scatter of the Charpy sized SE(B) specimens in the ductile-to-brittle transition regime. In this regime, according to the ELB and MC methods, SE(B) specimens provide cleavage toughness data, which tend to be non-conservative compared to those of standard C(T) specimens. However, analyses based on the exponential curve fitting method show good agreement between the fracture toughness estimates for the C(T) and Charpy size SE(B) specimens. At the lower bound toughness level (5% cleavage failure probability), corresponding to J=100 N/mm, the ductile-to-brittle transition curves of SE(B) specimens are reduced by 5–8 °C compared to those of standard C(T) specimens according to the MC-method. A constraint correction function for SE(B) specimens is presented that can be used to make cleavage toughness data of SE(B) specimens compatible with those of standard C(T) specimens.

Prediction of cleavage fracture in ferritic steels: a modified Weibull stress model

A modified three-parameter Weibull stress model is proposed in this paper, which considers the conjoint influences of plastic strain and stress triaxiality in the region of the crack tip. The model parameters are calibrated using two sets of fracture toughness data obtained from specimens exhibiting different constraint conditions at fracture, namely, deep-cracked compact tension specimens and shallow-cracked single-edge bending specimens. The master curve method is used to relate the fracture toughness data obtained at the different test temperatures. The calibrated Weibull stress model is then used to predict the cumulative failure probability of cleavage fracture for specimens containing surface cracks and loaded in varying combinations of tension and bending. The model predictions capture the measured toughness distributions for both bolt-loaded and pin-loaded specimens, while concurrently revealing a strong influence of the difference in crack tip constraint, due to different mode of loading, on probability of failure by cleavage. This effectively proves the applicability of the modified model for predicting cleavage-type fracture in ferritic steels.

Zircaloy-4 핵연료 피복관의 신파괴인성 시험법

To define the causes of cladding degradation which can take place during the operation of nuclear power plants, it is required to develop the new fracture toughness test of spent fuel cladding. The fracture toughness of Zircaloy-4 cladding was estimated using the recently developed KAERI embedded Charpy (KEC) specimen. Axially notched KEC specimens cut directly from unirradiated fuel claddings, were tested in a way similar to the standard toughness test method of a Single Edge Bending (SEB) specimen. The results of KEC fracture toughness test at room temperatures were discussed and compared with those of the previous other studies. In conclusions, even though the KEC fracture toughness test of nuclear fuel claddings was easier and more reliable than those developed earlier, the results from the cladding fracture tests were not the material characteristics but the specific fracture<br/> parameters which were deeply related to the specification of claddings. In addition, the phenomenon of<br/> a thickness yielding was not observed from the fracture surface. It was closely related to the fact that the plane strain condition of the KEC specimen was changed to the plane stress condition during crack advancing. It was also supported by the fractographic evidence that the formation of ductile dimples at the crack initiation became the similar appearance such as a quasi-cleavage after the sufficient crack advancing.<br/>

Experimental techniques for fracture instability toughness determination of unidirectional fibre metal laminates

The aim of this work is to propose procedures for the measurement of the fracture toughness of fibre metal laminates (FMLs) reinforced with unidirectional fibres of aramid or glass. Experimental techniques for fracture toughness evaluation by using Compact (C(T)) and Single-Edge Bend (SE(B)) specimens obeying ASTM standards are introduced. Procedures from the standard for thick metallic materials were modified in order to overcome problems, which can arise when testing FMLs – that is, specimen buckling, indentations and crack growth in planes other than the plane of the fatigue pre-crack or notch. The methodology proposed was experimentally tested leading to satisfactory results.

Numerical modelling of fracture initiation in large steel specimens at impact

Dynamic mode I fracture initiation in impact loaded single edge bend specimens with a quarter notch is investigated by numerical modelling and the results are compared with sets of experimental data from two different steel qualities. The finite element analysis include 2D (two-dimensional) plane strain, 2D plane stress and 3D models. No crack growth is included in the calculations. The impact velocities are approximately 15, 30 and 45 m/s and the specimen size is 320×75 mm 2 with a thickness of 20 or 40 mm. Some specimens have side grooves. Details of the deflection of the specimens are accurately reproduced prior to crack initiation both by the 2D plane strain model and by the 3D model. The experiments were performed in the ductile to brittle transition region. It is assumed that cleavage fracture initiation can be predicted by the Ritchie–Knott–Rice (RKR) model, i.e. cleavage fracture initiates when the opening stress exceeds the macroscopic cleavage stress over a fixed, critical distance. At an impact velocity of 15 m/s, fracture initiation by void nucleation and growth is observed, though the RKR-conditions is seemingly fulfilled according to the computational results. Possible limitations in the use of the RKR model are discussed.

Dynamic crack propagation in large steel specimens

Dynamic fracture experiments on crack initiation and crack growth in single edge bend specimens are performed. The impact velocity is in the range of 14 to 50 m/s and the specimen size is 320×75 mm with a thickness varying from 18 to 40 mm. The experiments are recorded by high speed photography. Two different steel qualities are investigated and their constitutive characterisation are obtained from uni-axial tension tests and shear tests with strain rates in the range 10 −4 to 10 3 s −1 and tension tests at temperatures between −196 and 600°C. One of the materials exhibits a transition from a ductile dimple fracture to a brittle cleavage fracture as the loading velocity increases and as the specimen thickness increases. Scanning electron microscope fractographs show that the density of plastic bridges within cleavage ligaments decreases with increasing impact velocity and with increasing specimen thickness. It is also noted that the local crack propagation direction deflects from the global one in cleavage fracture areas with a high density of plastic bridges. The other material fails in a ductile mode in all the investigated cases.

Fracture Micromechanisms of Fibre-Metal Laminates: In-Situ SEM Observations

The monotonic fracture micromechanisms of an aramid-aluminum laminate were studied using very small single edge bend specimens, SE(B) tested in a small-instrumented testing machine inside a scanning electron microscope. Thefracture process was followed by simultaneous observation of the sample and recording the loading variables. The instability fracture toughness was strongly dependent on the fibre-reinforced epoxy layer and the crack-growth in the external aluminum layers, prior to fracture instability, was influenced by the notch acuity. The load versus loadline displacement behaviourand load instabilities were similar to the ones obtained by conventional testing procedures. The technique implemented proved to be a powerful tool to study the fracture micromechanisms of aramid-aluminum laminates or other fibre-metal laminates and to correlate them with the recorded macro events.

INFLUENCE OF PARTICLE SIZE AND VOLUME FRACTION ON DAMAGE AND FRACTURE IN Al–Al3 Ti COMPOSITES AND MICROMECHANICAL MODELLING USING THE GTN MODEL

Six different Al–Al3 Ti composites were prepared via the powder metallurgy route. The size and volume fraction of Al3 Ti particles was varied for a systematic investigation of fracture behaviour. The dominant failure mechanism in the composites is particle fracture and void growth starting from the broken particles. In comparison with the pure Al–matrix, an incorporation of Al3 Ti particles reduces the crack initiation toughness and reduces the slope of the crack growth resistance curve. The inter‐particle distance was found to be the main microstructural parameter controlling the slope of the crack growth resistance curve. The modified Gurson–Tvergaard–Needleman model (GTN model) was applied to one of the composites. The behaviour of tensile specimens could be successfully modelled, whereas the experimentally observed crack propagation in precracked single edge bend specimens [SE(B)] could not be simulated with the GTN model.