Three-point Bend Specimens Research Articles

An Industrial Approach to High Strain Rate Testing

Some industrial applications require properties of materials to be determined to evaluate components’ safety in the event of loading and impact. Understanding the behaviour of materials subjected to extreme dynamic loading will aid in enhancing their design. This work is based on developing methods to appraise high loading rate measurements. Different approaches to quantify material properties such as finite element method (FEM), instrumented Charpy testing, and impact testing using servo-hydraulic testing machines are included. Testing is performed at various loading rates, extending existing quasi-static fracture toughness determination to higher loading rates, and accounting for strain-rate dependent properties. The high loading rate servo-hydraulic test machine located at TWI, Cambridge has the capacity to test up to a displacement rate of 20 m/s. The force, displacement, and time parameters are captured by Digital Image Correlation (DIC), which improves the accuracy of the results obtained from experiments. Moreover, the underlying plasticity theory to capture the influence of the strain rate is presented, along with damage constants for FEM calculations adopting the Johnson-Cook model. In addition to the Johnson-Cook approach, analytical solutions using dislocation evolution theory were applied which features the effects of phonon drag and dynamic recovery coefficient in body-centered cubic materials of which X65 grade steel was applied. Also, a deep learning framework was built to predict the tensile curves when given specific test conditions and sample specifications. It was found that high strain rate tests lead to local change at the crack tip which increases plasticity and reduces fracture toughness with single-edged notched three-point bend specimen. The yield strength of the material increased with loading rates during tensile testing leading to a ductile to brittle transition of metals. These strategies were used to establish a revised approach for high strain rate testing and predicting stress-strain curves with a machine learning algorithm.

Experimental investigation of tubular crushing and tubular bending of TWB application in automotive vehicles for frontal crash

Study of crashworthy structures is the key realm of attention for many researchers from the last few years now. The main intention for developing the structures with better energy-absorbing ability has led the many researchers to carry out analysis using experimental and simulation methods. The lightweight design is also a fairly challenging issue in the vehicle industry. Application of tailor welded blanks is the most effective methods to attaining reduce the weight effectively with the improved safety of structure. The present research is to study the tailor welded blank applications in automotive vehicles for frontal crash validation by three-point tubular bending specimens and tubular structure crushing specimens. A series of TWB tubes with different thickness combinations are carried out to test the crushing test evaluation. The TWB specimens are fabricated through the laser welding process. In experimental analysis, the indicators of the crashworthiness are analyzed, which are Energy Absorption, Peak Crushing Force, Average Crush Force, Specific Energy Absorption, Crush Force Efficiency, and Average Bending Movement. Thus, the analysis shows that the TWB is definitely effective and feasible for vehicle lightweight designing.

Research on Creep Behavior of Three-Point Bending Specimen With Fixed Constraints at the Large Deformation Stage

Abstract Three-point bending specimen with fixed constraints is a novel small specimen test technique, which can simultaneously obtain creep deformation and creep fracture data. However, the current research only focused on the small deformation theoretical analysis, which is contrary to the actual experiment results. In this study, the general deformation theory was introduced to analyze creep deformation behavior of three-point bending specimen with fixed constraints at the large deformation stage. Based on this theory, the equivalent stress and strain were analyzed. Then, the feasibility and accuracy were verified by comparing with the experimental data of A7N01 aluminum alloy at 380 °C. The results show that the regressed creep parameters agree well with those from the uni-axial ones. It can be found that the equivalent stress obtained by the general deformation theory can be well used to life prediction analysis of A7N01 aluminum alloy.

Mechanical Characterization and Fracture Behavior of Extruded ZK60A Magnesium Alloy

The current study addresses the mechanical and fracture behaviors of extruded ZK60A magnesium alloy. This material has numerous potential structural applications, and its characteristics need to be determined for it to be used as a structural material. Tensile, hardness, and Charpy impact tests were performed as per American Society for Testing and Materials standards to determine the mechanical behavior of the material. Its fracture behavior was determined using plane-strain fracture toughness, stable crack growth, and fractographic tests. The fracture toughness was calculated from the fracture toughness–thickness curve obtained from fracture tests on single-edge notch bend specimens with fatigue pre-cracks. The stable crack growth studies were conducted using three-point bend specimens to determine the initiation and maximum loads and the range of stable crack growth for both mode I and mixed-mode loading cases. X-ray diffraction analysis of the alloy was also conducted. Scanning electron microscopy was used to observe the fracture surface morphologies of the specimens. This study addresses the structural analysis, advanced materials, and safety and reliability aspects of aerospace research.

Influence of specimen geometry on fracture toughnesses of concrete based on boundary effect model

This paper presents the effect of specimen geometry on fracture characteristics of concrete in terms of fracture toughness KIc and initial fracture toughness KIcini. Three commonly used specimen geometries in laboratory were adopted in the study, that is, three-point bending (TPB), compact tension (CT) and four-point bending (FPB) specimens. The Boundary Effect Model (BEM) was used to determine these two fracture parameters, where a new approach was proposed to derive KIcini. To do this, only the maximum aggregate size dmax, the maximum load Pmax and the initial crack length relative to the specimen depth α0 were required. Previous experiments from TPB, CT and FPB specimens were reutilized to acquire KIc and KIcini, and then the geometry influence on these two fracture toughnesses were investigated. The results show that the gained values of KIc and KIcini from TPB, CT, FPB separately or combined TPB + CT + FPB were rather close, meaning little influence from specimen geometry on fracture toughness. Additionally, the ratio of KIcini/KIc was almost the same regardless of specimen geometry shape and α0 when 0.2 ≤ α0 ≤ 0.8.

Experimental and Numerical Investigation on Specimen Geometry Effect on the CTOD Value For VL-E36 Shipbuilding Steel

Abstract There are special cases in the marine industry, where additional material tests, such as the fracture toughness test, must be performed. Additional fracture toughness tests, such as CTOD (Crack Tip Opening Displacement), are typically performed on three-point bend specimens. The dimension that defines all the specimen dimensions is the thickness of the material to be tested. It is recommended by classification societies (e.g. DNVGL) to test specimens that are twice as high as the material thickness. The width determines the length and, therefore, the weight of the specimen which, for a 100 mm plate is over 140 kg. Current ASTM E1820, BS7448-1 and ISO 12135 testing standards also allow for proportions other than those recommended. This results in a much smaller test piece. Reducing the specimen size allows the testing machine to achieve lower forces than a specimen with a width to thickness ratio of two. This paper presents the effect of changing the specimen geometry on CTOD test results. Research was performed for specimens with a height to thickness ratio of one and two. Abaqus software was used for numerical calculations. The numerical results were, at selected points, verified experimentally.

Comparison of Testing Method Effects on Cracking Resistance of Asphalt Concrete Mixtures

As an inherent characteristic of materials, the fracture toughness is an important parameter to study the cracking behavior of asphalt concrete mixtures. Although material compositions and environmental conditions have a significant effect on the fracture toughness, for a certain material and testing environment, the test condition including the specimen configuration and loading type may also affect the obtained fracture toughness. In this paper, the effect of specimen configuration and applied loading type on the measured pure mode-I fracture toughness (KIc) is investigated. In order to achieve this purpose, using a typical asphalt mixture, four different test specimens including Semi-Circular Bend (SCB), Edge Notch Disc Bend (ENDB), Single Edge Notch Beam (SENB) and Edge Notch Diametral Compression (ENDC) disc are tested under pure mode I. The mentioned specimens have different shapes (i.e., full disc, semi-disc and rectangular beam) and are loaded either with symmetric three-point bending or diametral compressive force. The tests were performed at two low temperatures (−5 °C and −25 °C) and it was observed that the critical mode-I fracture toughness (KIc) was changed slightly (up to 10%) by changing the shape of the test specimen (i.e., disc and beam). This reveals that the fracture toughness is not significantly dependent on the shape of the test specimen. However, the type of applied loading has a significant influence on the determined mode I fracture toughness such that the fracture toughness determined by the disc shape specimen loaded by diametral compression (i.e., ENDC) is about 25% less than the KIc value with the same geometry but loaded with the three-point bending (i.e., ENDB) specimen. In addition, the fracture toughness values of all tested samples were increased linearly by decreasing the test temperature such that the fracture toughness ratio (KIc (@−25 °C)/KIc (@−5 °C)) was nearly constant for the ENDB, ENDC, SCB and SENB samples.

Stress intensity factors for micro- and macroscale bimaterial cantilevers and bend specimens

Bilayered materials with different properties play an important role in several fields of engineering to improve the mechanical, thermal, electrical, magnetic characteristics of structures. In order to determine the fracture toughness of such bimaterials, experimental measurements must be combined with numerical calculations, which is a tremendous effort. Therefore, a procedure is presented which enables a simple determination of the (critical) stress intensity factor for bimaterial bend specimens. The procedure is applicable for nano- to macroscale cantilevers and three-point bend specimens consisting of linear-elastic or elastic-plastic film and substrate materials. By finite element computations, the procedure is verified for a wide range of Young's moduli combinations, layer heights, and crack lengths. Possible limitations of the procedure are worked out. Practical applications for concrete bimaterial systems are presented, as well as the usage as a failure assessment tool.

Mechanical Testing and Modeling of the Time-Temperature Superposition Response in Hybrid Fiber Reinforced Composites.

The purpose of this study was to manufacture hybrid composites from fabrics with superior ballistic performance, and to analyze their viscoelastic and mechanical response. Therefore, composites in hybrid lay-up modes were manufactured from Vectran, Kevlar and aluminum fiber-woven fabrics through a vacuum assisted resin transfer molding. The specimens were consequently analyzed using static three-point bending, as well as by dynamic mechanical analysis (DMA). Apart from DMA, time–temperature superposition (TTS) analysis was performed by all available models. It was possible to study the intrinsic viscoelastic behavior of hybrid ballistic laminates, with TTS analysis gained from creep testing. A polynomic mathematical function was proposed to provide a high accuracy for TTS curves, when shifting out of the linearity regimes is required. The usual Williams–Landel–Ferry and Arrhenius models proved not useful in order to describe and model the shift factors of the acquired curves. In terms of static results, the highly nonlinear stress–strain curve of both composites was obvious, whereas the differential mechanism of failure in relation to stress absorption, at each stage of deformation, was studied. SEM fractography revealed that hybrid specimens with Kevlar plies are prone to tensile side failure, whereas the hybrid specimens with Vectran plies exhibited high performance on the tensile side of the specimens in three-point bending, leading to compressive failure owing to the high stress retained at higher strains after the maximum bending strength was reached.

The Influence of Different Constitutive Model Relations on Mechanical Behavior of Crack Tip Plastic Zone

For ductile materials with cracks, when the stress at crack tip exceeds the yield strength, a plastic zone will be formed around crack tip. In this paper, the extended finite element method(XFEM) in ABAQUS was used to simulate the crack, and the mechanical behaviors of crack tip plastic zone under different constitutive models were studied by taking the three-point bending specimen as the research object. The COD experiment and theoretical verification of three-point bending demonstrate the effectiveness of this method. The effect of the plastic modulus on size of crack tip plastic zone under the double broken line constitutive model is analyzed, and the effects of the load on plastic zone size and stress distribution near crack tip under the true stress-strain constitutive model is discussed. Finally, the difference of stress distributions around crack tip obtained from two constitutive models is compared.

Laboratory-scale mixed-mode I/II fracture tests on columnar saline ice

Laboratory-scale experiments on mixed-mode I/II (including pure modes I and II) fracture of non-oriented columnar saline ice were performed. In the experiments, obliquely notched, three-point bending specimens were used, with the load applied in the direction perpendicular to the columnar grains. Tests were performed on dry isothermal (−10 °C) specimens and specimens floating in water and having a temperature gradient (mean temperature: −2.5 °C). The fracture loads and crack initiation angles were analyzed. The apparent mode I, mode II and mixed-mode fracture toughness and the flexural strength of the floating and relatively warm specimens were only about thirty percent of those of the dry and cold specimens. The results showed that the T-stress significantly influenced the mixed-mode I/II fracture of ice; good agreement was found between the experimental results and those predicted using the generalized maximum tangential stress criterion. Both trans- and inter-granular crack growth were observed, regardless of the specimen type or mode of loading.

Effect of imidazoline inhibitor on stress corrosion cracking of P110 steel in simulated annulus environments of CO2 injection well

• The SCC of a P110 steel in a simulated annulus environment has been investigated. • Inadequate dose of imidazoline inhibitor will greatly increases SCC susceptibility. • The application of corrosion inhibitor to control SCC should be carefully considered. In this study, the effect of imidazoline inhibitor on the stress corrosion cracking (SCC) behavior of P110 steel in a simulated annulus environment in CO 2 injection wells was investigated by immersion tests on three-point bending specimens, electrochemical measurements, and corrosion morphology analysis. Results show that the addition of imidazoline inhibitor may lead to a high sensitivity of SCC for P110 steel. In the absence of tensile stress, P110 steel gains effective protection when the corrosion inhibitor concentration is less than 1000 mg/L. However, under various tensile loadings, the SCC susceptibility, which in the presence of the inhibitor is higher than that in the absence of the inhibitor, increases with an increase in the concentration of the inhibitor (when the inhibitor concentration is less than 1000 mg/L). The SCC sensitivity starts to reduce if the inhibitor is added continuously; when the inhibitor concentration reaches 2000 mg/L, SCC becomes markedly suppressed. The above phenomenon manifests that the addition of an inhibitor needs careful consideration and the SCC test must be introduced to evaluate the efficiency of the inhibitors; electrochemical analysis and immersion tests of non-SCC samples alone are insufficient to assess the controlling efficiency of inhibitors.

Improved discrete element numerical simulation and experiment on low-temperature anti-cracking performance of asphalt mixture based on PFC2D

To study the cracking law of asphalt mixtures at low temperature, an improved mesoscopic model of an asphalt mixture Marshall split specimen and three-point trabecular bending specimen were established based on the discrete element method using PFC2D. Secondly, by defining and assigning the bonding constitutive model between different particles in the asphalt mixture, the numerical simulation results of AC-13 and AC-16 continuous, dense-graded asphalt mixtures’ splitting and three-point beam bending at −10 °C were analyzed. The experiment verified that the reliability of the numerical model described herein improved. The results showed that the two-dimensional model of an asphalt mixture based on the discrete element method can simulate the splitting and three-point beam bending test of asphalt mixtures with different gradations. Contact fracture between aggregate and asphalt mortar is the principal reason that an asphalt mixture cracks. Further, the contact between the aggregates contributes the most to the asphalt mixture’s splitting strength, and the contact between the asphalt mortar and the asphalt mortar and the aggregate contributes more than 85% to the asphalt mixture’s flexural tensile strength. In addition, the asphalt mixture’s splitting strength and flexural tensile strength increased as the maximum nominal particle size in the asphalt mixture gradation increased. Therefore, the results of this study can provide a theoretical basis for the design of asphalt pavement materials.

A new approach to evaluate material creep properties by C-shape ring specimen with fixed constraints

Small specimen test technique is widely used to evaluate material creep properties for those components operated at the elevated temperatures. However, the existing small specimen test techniques cannot be well applied for small miniature tubular components well, such as steam pipe and gas turbine recuperator in aviation, due to the equivalent gauge length, specimen volume, stress analysis method and conversion relationship. In this paper, combing the advantages of three-point bending specimen with fixed constraints and small ring creep specimen, a new C-shape ring specimen with fixed constraints (CRSFC) was proposed. Based on beam bending model, the conversion relationship between CRSFC and uniaxial creep test data was established by using complementary strain energy and reference stress method. Using finite element method, conversion coefficients and stress evolution process were obtained. Then the feasibility and accuracy of the above conversion relationship were verified by carrying out four sets of CRSFC creep tests of 1.25Cr0.5MoSi at 550 °C. It can be seen that creep parameters obtained by CRSFC agree well with those from uniaxial creep test with the maximum error of 22.6%. Finally, the effects of the straight edge length, indenter radius, eccentric load and indenter-specimen surface friction coefficient on the load-point steady-state displacement rate were investigated by finite element method. The results show that the effect of the straight edge length is negligible. In order to minimize the effects of other parameters, the indenter radius 0.6 mm ≤ r ≤ 1.2 mm, eccentric displacements e ≤ 0.2 mm and friction coefficient f ≤ 0.8 are recommended in CRSFC creep test.

Crack onset in stretched open hole PMMA plates considering linear and non-linear elastic behaviours

Crack onset in PMMA holed plates subjected to tensile stresses is studied experimentally and by the coupled stress and energy criterion of the Finite Fracture Mechanics (CCFFM). The elastic, strength and fracture properties of PMMA are determined by the standard tests, a clearly nonlinear stress-strain relation being identified in the tensile tests. Thus, a novel numerical implementation of the CCFFM considering a non-linear elastic (NLE) material model, using the Ramberg-Osgood approximation, in addition to the usually used linear elastic (LE) model, is developed. Testing of plates with different hole sizes shows a hole size effect in the nominal failure load as expected. For a better fitting of the experimental results, higher strength values obtained by three point bending (TPB) flatwise and edgewise coupons (without any notch), for these material models, are used, apparently for the first time, in the CCFFM predictions. This approach reflects the observation that the strength values associated to smaller but highly stressed volumes, like those located at stress maxima in the holed plates and TPB specimens, are higher. For finite-width holed plates and both material behaviours, suitable FEM models are developed to implement the CCFFM for both LE and NLE models, considering plane stress state. Moreover, an inverse procedure is devised, using the experimental data for holed plates and predictions by CCFFM, to estimate the strength and fracture properties to be used in both material models, providing very good correlations of the CCFFM predictions with the experimental results.

Methodology for calculating J-integral range [formula omitted] under cyclic loading

The J-integral range or the cyclic J-integral, ΔJ, is frequently utilized to deal with the fatigue crack growth of ductile materials with large scale yielding. ΔJ was originally defined as a line integral similar to the J-integral proposed by Rice. Many researchers correlated fatigue crack growth rate of ductile materials with ΔJ defined by Jmax−Jmin. Although it is theoretically shown that the latter definition of ΔJ, that is, ΔJ=Jmax−Jmin, is not equivalent to the former defined by a line integral, why is the latter definition of ΔJ utilized so frequently? This question is main concern of the present paper. To answer this question, we derive the expression of ΔJ represented by a line integral for HRR singular fields, which govern the vicinity of a crack tip under large scale yielding, then formulate the difference between the ΔJ represented by a line integral and ΔJ=Jmax−Jmin. We perform the error estimation for three-point bending specimens to clarify how accurately (Jmax−Jmin) predicts the ΔJ-value, compared with the ΔJ represented by a line integral, which is supposed to provide the exact ΔJ-value. As a result, theΔJ-value calculated from (Jmax−Jmin) is identical to the ΔJ-value calculated from a line integral in the case of the zero-tension cyclic loading conditions, and the deviation between the former and latter values is small under near zero-tension and large cyclic loading amplitude conditions. The use of the ΔJ defined by (Jmax−Jmin) should be limited to the cases where near zero-tension and large cyclic loading amplitude conditions are satisfied.

Analysis of Mixed-Mode I/II/III Fracture Toughness Based on a Three-Point Bending Sandstone Specimen with an Inclined Crack

The crack-propagation form may appear as an arbitrary mixed-mode fracture in an engineering structure due to an irregular internal crack. It is of great significance to research the mixed-mode fracture of materials with cracks. The coupling effect of multiple variables (crack height ratio, horizontal deflection angle and vertical deflection angle) on fracture parameters such as the stress intensity factors and the T-stress are the key points in this paper. A three-point bending specimen with an inclined crack was proposed and used to conduct mixed-mode fracture research. The fracture parameters were obtained by finite element analysis, and the computed results showed that the pure mode I fracture and mixed-mode fractures (mode I/II, mode I/III and mode I/II/III) can be realized by changing the deflection angles of the crack. The pure mode I and the mixed-mode fracture toughness of sandstone were obtained by a series of mixed-mode fracture experiments. The experimental results were analyzed with the generalized maximum tangential strain energy density factor criterion considering T-stress. The results showed that the non-singular term T-stress in the fracture parameters cannot be ignored in any mixed-mode fracture research, and the generalized maximum tangential strain energy density factor criterion considering T-stress can better predict the mixed-mode fracture toughness than other criteria.

Effects of span-depth ratios on the energy release rate for three-point bending beams

The effects of span-depth ratios on the energy release rate for three-point bending beams were examined. Expressions for the energy release rate for three-point bending specimens with various span-depth ratios were developed using linear interpolation method. The double-G fracture parameters were calculated through tests of three-point bending beams with the same span (800 mm) but various depths (100 mm, 150 mm, 200 mm, 250 mm and 300 mm) and the findings in literature. Results indicate that (1) with increasing the span-depth ratio, an almost constant initial fracture energy release rate was obtained, and slight decrease tendency of the unstable energy release rate was observed; (2) The empirical relationship between the initial fracture energy and total fracture energy suggested in size effect model was conformed using the unstable fracture energy release rate which was the same as the initial fracture energy; (3) Equivalence between double-G and double-K fracture model was verified; (4) Moreover, the analytical results of unstable fracture energy release rate exhibited a good consistency with the experimental ones, which were insensitive to the softening function.

Determination of crack extension resistance of concrete from boundary effect model

The fracture behavior of concrete can be described by an R-curve, which represents the ability of concrete to resist crack propagation. In this study, the R-curve is defined as the envelope of the energy release rates in the critical state and is constructed on the basis of the boundary effect model. Two fracture parameters are introduced for constructing the R-curve, namely, the fracture energy Gf and the equivalent crack extension cf in an infinitely large specimen, and these two vital parameters can be obtained from testing specimens of different sizes. One of the greatest features of the proposed R-curve is that the influence of concrete aggregate is explicitly manifested in the R-curve expression in terms of the maximum aggregate size. The theoretically derived ascending branch of the R-curve is fitted using a unified function for three-point bending specimens with varying values of the initial crack length relative to the specimen depth (between 0.2 and 0.9). The developed R-curve approach is applied to the tested three-point bending notched concrete beams, and the predicted load-displacement responses are found to agree with the experimental curves. It is also shown that the results are not sensitive to the choice of the discrete number β, which is included in the R-curve expression to address the linkage between the fictitious crack growth and coarse aggregate structures of concrete.

Fracture-mechanical properties of neutron irradiated ITER specification tungsten

The work focuses on the investigation of the influence of neutron irradiation on the fracture mechanical properties of ITER specification-conform, stress-relieved tungsten bar. The irradiation of miniaturized Three-Point Bend specimens was performed inside the fuel channel of the Material Test High Flux BR2 reactor of SCK•CEN in Mol. An irradiation damage dose close to 1 dpa (in tungsten) was achieved at 800°C with active temperature cooling and constant on-line temperature monitoring. Thick-wall stainless steel capsules were implemented for shielding the thermal neutrons in order to reduce Re transmutation down to ~2 at.% (and 0.2 at.% Os). The quasi-static fracture mechanical experiments were carried out following ASTM E399 aiming at the determination of plane strain fracture toughness KIc. The post irradiation examination of the specimens irradiated at 800°C reveals severe material embrittlement. At Ttest = Tirr = 800°C, a deformation free brittle fracture is observed. The fractographic investigations show a mixture of brittle transgranular cleavage and intergranular fracture. With increasing the test temperature above 1000°C, the fracture mode is changed from the brittle to a ductile one. Blunting of the notch tip leads to a suppression of the crack initiation and propagation and consequently no failure of the specimens was observed up to severe deflection levels. In some cases, however, a ductile crack growth with a characteristic dimple formation was identified, in addition. Based on the obtained results, the Ductile to Brittle Transition Temperature shift induced by the neutron irradiation at 800°C is evaluated to be 600-625°C.