Single Edge Notch Tension Research Articles

Experimental and numerical assessment of fracture toughness variations in steam boiler components after a long period of operation

This study presents an experimental and numerical assessment of the fracture toughness of steam boiler components, which have been in operation for more than 100,000 h. The materials tested are components of two different parts of a steam turbine unit: the pipeline section that connects the headers with turbines, which is made of 13HMF steel, and the valve chamber section, which is made of L17HMF steel grades. Full-size arc-shaped tension specimens (AT) are employed for the experimental evaluation. AT and single-edge notch tension (SENT) specimens are used for numerical assessment. The finite element method (FEM) formulations are developed and examined in Abaqus, which is set up as a shell model with the specimen thickness designated as the mid-surface for the analysis. The notch is modeled using a contour integral definition based on the maximum energy release rate criterion. The fracture toughness is quantified using the stress intensity factor (KI), and the results are compared. The valve chamber is found to have a higher fracture toughness than the pipeline section. The effect of specimen geometry is also noticeable, and the fracture toughness of SENT and AT specimens are compared. The results are useful in assessing the component's durability after long operation.

Research on Crack Propagation of Nitrate Ester Plasticized Polyether Propellant: Experiments and Simulation.

To understand the fracture properties of the nitrate ester plasticized polyether (NEPE) propellant, single-edge notched tension (SENT) tests were carried out at room temperature (20 °C) under different tensile rates (10-500 mm/min). The mechanical response, crack morphology, evolution path, and crack propagation velocity during the fracture process were studied using a combination of a drawing machine and a high-speed camera. The mode I critical stress intensity factor KIc was calculated to analyze the tensile fracture toughness of the NEPE propellant, and a criterion related to KIc was proposed as a means of determining whether the solid rocket motors can normally work. The experimental results demonstrated that the NEPE propellant exhibited blunting fracture phenomena during crack propagation, resulting in fluctuating crack propagation velocity. The fracture toughness of the NEPE propellant exhibited clear rate dependence. When the tensile rate increased from 10 mm/min to 500 mm/min, the magnitude of the critical stress intensity factor increased by 62.3%. Moreover, numerical studies based on bond-based peridynamic (BBPD) were performed by modeling the fracture process of the NEPE propellant, including the crack propagation speed and the load-displacement curve of the NEPE propellant. The simulation results were then compared with the experiments.

Novel semi-analytical model for solving the C*-integral of specimens with mode-I crack under various constraints

The energy rate line integral C* is an essential fracture parameter that characterizes the stress and strain rate field intensity at a crack tip for materials undergoing creep deformation, and is also a crucial parameter describing the creep crack growth rate. This study proposes a method for determining the characteristic parameters of the creep displacement rate model for specimens with mode-I crack under various constraints. Based on the displacement rate model, a semi-analytical model of the C*-integral related to the displacement rate, load, specimen sizes, and Norton's law parameters of materials is proposed. Furthermore, finite element analysis (FEA) models were established for compact tension (CT), single-edged notched bending (SEB), C-shaped tension (CST), and single-edge notched tension (SET) specimens, and the proposed models were verified using FEA results and those predicted by the ASTM method. The explicit correlation between the creep displacement rate and crack length a in the model can contribute to developing novel testing methods for real-time crack length and creep crack growth rate.

On the suitability of single-edge notch tension (SENT) testing for assessing hydrogen-assisted cracking susceptibility

Combined experiments and computational modelling are used to increase understanding of the suitability of the Single-Edge Notch Tension (SENT) test for assessing hydrogen embrittlement susceptibility. The SENT tests were designed to provide the mode I threshold stress intensity factor (Kth) for hydrogen-assisted cracking of a C110 steel in two corrosive environments. These were accompanied by hydrogen permeation experiments to relate the environments to the absorbed hydrogen concentrations. A coupled phase-field-based deformation–diffusion-fracture model is then employed to simulate the SENT tests, predicting Kth in good agreement with the experimental results and providing insights into the hydrogen absorption–diffusion–cracking interactions. The suitability of SENT testing and its optimal characteristics (e.g., test duration) are discussed in terms of the various simultaneous active time-dependent phenomena, triaxiality dependencies, and regimes of hydrogen embrittlement susceptibility.

On the validity of the Tada stress intensity factor solution for the single edge notch tension specimen with pinned ends

The validity of the Tada stress intensity factor (KTada) for pinned-ends single edge notch tension [SEN(T)] specimens is assessed via a combined experimental-modeling approach. Analysis of fatigue crack growth rate reductions during constant-ΔKTada loading demonstrates that specific combinations of alloy stiffness, geometry, and loading result in the true K deviating below KTada. Geometrically non-linear, 3-dimensional finite element calculations confirm mild-to-strong influences of these parameters, which are not captured by KTada. Most existing pinned SEN(T) data are found to use parameters where KTada is not significantly reduced, but the present results underscore the need for a more broadly applicable K solution.

The effect of hydrogen and notch orientation in SENT specimens on the fracture toughness of an API 5L X70 pipeline steel

Transporting hydrogen gas through pipelines is an important topic within the context of energy transition. An essential challenge hereto is the phenomenon of hydrogen embrittlement of pipeline steels which includes a reduction in fracture toughness. As the theories accounting for hydrogen embrittlement are still debated, improving fundamental insights into the underlying mechanisms is crucial. Fracture toughness tests on single edge notched tension (SENT) specimens have been performed to examine the influence of hydrogen on the fracture behavior of a pipeline steel. An API 5L X70 steel was selected for this purpose, characterized by a distinctive banded microstructure commonly seen in pipeline steels. The test specimens were extracted from the steel pipe, and a notch in two different orientations was machined. By using a combination of fractography and X-ray micro-CT (Computed Tomography), the fracture mechanisms are revealed. The tearing resistance characteristics of the steel, with and without the presence of hydrogen, are demonstrated through tearing resistance curves. The experiments show that the banded microstructure plays a key role in the results through the development of splits at the microstructural bands. While these splits are also present in uncharged toughness test specimens, they are increasingly present in hydrogen charged specimens suggesting a hydrogen related weakening of the banded microstructure. In addition, it is demonstrated that hydrogen induces an increasingly zigzagged crack path. This is attributed to a potential combination of accelerated void nucleation at the microstructural bands, and accelerated shear-driven fracture.

Plastic Zone Radius Criteria for Crack Propagation Angle Evaluated with Experimentally Obtained Displacement Fields

The monitoring and maintenance of cracked structures are generally carried out using structural integrity assessments. The plastic zone (PZ) crack path (CP) criteria state that a crack grows in a specific direction when the radius of the plastic zone ahead of the crack tip reaches a minimum value. The PZ can be evaluated using stress intensity factors (SIFs). The SIFs under mixed-mode loading were extracted from the literature from three samples: two single edge notch tension (SENT) samples (E = 2.5 GPa, v = 0.38) made from polycarbonate and one modified compact test (C(T)) sample made from low-carbon steel (E = 200 GPa, v = 0.3). In addition, the CP angle was evaluated for the W and R criteria with experimental data, which included non-linear effects such as fatigue-induced plasticity, crack roughness, and debris. It was found that both can predict the CP for lateral cracks in both tested materials and monotonic and cyclic load when the mode mixity does not change considerably from one crack length to the next or goes beyond 0.2. Moreover, the R criterion exhibited an error as high as 1.7%, whereas the W criterion showed a 6% error on the last crack length for the low-carbon steel sample under cyclic load, which had a 100% increase in mode mixity. Finally, the applicability of LEFM was checked, while the CP was sought by finding the size of the PZ.

Effect of specimen thickness on fatigue crack shape evolution for aluminum alloy

The investigation of fatigue crack propagation and fracture mechanisms in high-thickness metal plates holds pivotal importance in the advancement of a three-dimensional damage tolerance assessment methodology. This research also bears significant implications for ensuring the safe operation of large-scale mechanical equipment. In this study, we examine the influence of specimen thickness on the evolution of fatigue crack shapes in an aluminum alloy. Fatigue crack growth tests were conducted on single-edge notch tension specimens to explore the impact of specimen thickness on the shape of fatigue crack growth. Additionally, we propose a calculation model for crack growth shape based on an energy model in this paper. Both experimental and analytical findings indicate that specimen thickness does indeed exert an influence on fatigue crack shape. Specifically, as the specimen thickness increases, the crack shape transitions from resembling a “fingernail” to a “saddle” shape.

Experimental characterization and phase-field modeling of anisotropic brittle fracture in silicon

We employ experiments and phase-field modeling to characterize the four-fold anisotropic elastic and fracture response of solar-grade monocrystalline silicon on the macro-scale using thin silicon wafers. Tension tests on unnotched and double edge-notched specimens are performed to characterize the in-plane four-fold symmetric elastic behavior of the material and its fracture toughness along the weak directions. Single edge-notched tension tests with the notch oriented along the strong direction are performed to induce crack zigzagging and qualitatively capture the inherent stochastic nature of crack propagation in this setting. With the experimental results, we calibrate two deterministic anisotropic fourth-order phase-field models considering anisotropy in both elastic and fracture energies, as well as their stochastic extension proposed in our previous work. Overall, the very good agreement between experimental and numerical results demonstrates the ability of phase-field modeling to quantitatively predict anisotropic brittle fracture in monocrystalline silicon. Remarkably, very different zigzagging crack patterns obtained on nominally identical specimens are naturally reproduced by the stochastic model.

Crack initiation and propagation behavior of dissimilar interface with intermetallic compound layer in Al/steel joint using coupled multiscale mechanical testing

We demonstrate multiscale mechanical testing using miniature and microscale tensile tests to elucidate the crack initiation and propagation behaviors corresponding to interfacial nanostructures in dissimilar joints of 6061 aluminum alloy and 304 stainless steel. The initial nucleation and subsequent growth of intermetallic compounds (IMCs) can be controlled by heat treatment after friction stir lap welding. The miniature tensile tests exhibited the relationship between the joint strength and IMC layer thickness with changes in the fracture location. Microscale tensile testing using a single edge-notch tension geometry initiates the crack and subsequent propagations near the interface, which helps identify the crack initiation site and understand the dependence of the local strength on the type of IMCs. Crack deviation behavior toward the Al side, attributed to the difference of local strength, is confirmed by in situ observations, which indicated that continuous failure can easily occur within the grown IMCs, particularly in macroscale joints. It was concluded that the crack propagation is controlled by the local crack deviation toward metal matrix, which tends to occur for the dissimilar interface with thin IMC layer. This miniature/microscale tensile testing approach is expected to clarify the essential relationship between the interfacial microstructure and the fracture behavior.

Further investigation of two-parameter J-A estimation for clamped SET specimens

Based on the J-A two-parameter characterization, this paper presents a systematic study of the crack-tip constraint for clamped single-edge notched tension (SET) specimens. Extensive finite element analyses (FEA) are conducted to obtain the A solutions for the modified boundary layer (MBL) model and the SET specimen. The material used in the analysis is the Ramberg-Osgood power-law material, with varying yield stress and strain hardening exponents. Based on previous studies, the T-stress-related A solutions for MBL problems under small-scale yielding conditions are obtained from FEA results, and the A solutions for the SET specimen are found to scale with normalized applied load under large-scale yielding conditions. By summing up these two solutions, the total A for the SET specimen can be estimated, covering the entire range from small-scale to large-scale yielding conditions. A key geometry factor is introduced as a function of material properties, crack depths and applied load. Some fitting equations are proposed in this estimation method, and a Python program is developed to quickly and accurately obtain the total A for the SET specimen. The results of the present study show good agreement for all the simulated cases. The proposed solutions of constraint parameter A can be used to establish the constraint-corrected J-R curve for SET specimens.

Selective laser sintered Pipe Ring Notched Tension specimens for examination of fracture properties of pipeline materials

In order to develop a non-standard method for determining the resistance to fracture and damage of pipeline materials, a new geometry of ring-shaped specimens with sharp notches or cracks has been defined. The need to develop a new method for testing of the specimens cut from the pipes arises due to the difficulties in determination of fracture mechanics parameters on thin-walled pressure pipelines, especially those with a smaller cross-section, by application of the standard procedures/specimens. Previous studies dealing with the topic of pipeline testing by non-standard methods are presented in the introductory part of the paper. In the experimental part of the research, tests on PRNT (Pipe Ring Notched Tension) and SENT (Single Edge Notched Tension) specimens are performed. Samples of these specimens were produced by SLS (Selective Laser Sintering) technique of additive production from PA12 (polyamide PA 2200) material. For the purpose of this study, a tool that is protected at the national level (in Serbia) as intellectual property is used for testing of the ring-shaped PRNT specimens. Tensile testing of both types of specimens is monitored by Aramis GOM 2M system; its operation is based on the method of digital image correlation, DIC. Additionally, finite element analyses are conducted on the PRNT and SENT geometries, enabling the calculation of the fracture mechanics parameter – Stress intensity factor K. It is concluded that the presented procedure based on the PRNT specimen has a good potential for use as a non-standard method for fracture resistance examination of pipeline materials. It can be performed on the specimens cut directly from the pipes (new or from exploitation). The dependence of the fracture resistance on the stress concentrator size is not pronounced, which means that the results depend dominantly on the material properties, rather than on geometry.

Experimental Evaluation of KIEAC of a Carbon Steel Using the Pin-Loaded SENT Geometry

Abstract The experimental determination of the threshold stress intensity factor for environment-assisted cracking (KIEAC) is described by several standards, which allow the use of different specimen geometries and methodologies for crack length estimation. In some cases, the combination of structure, specimen size, or both, main loading direction, and crack orientations of the component that need to be characterized limit the use of standardized geometries. Consequently, alternative geometries must be used. In this study, fatigue pre-cracked pin-loaded single edge notched tension specimens as defined by BS 8571:2018, Method of Test for Determination of Fracture Toughness in Metallic Materials Using Single Edge Notched Tension (SENT) Specimens, were applied for the experimental evaluation of the KIEAC of a carbon steel. The specimens were tested in deaerated substitute ocean water solution saturated with carbon dioxide at 40°C and at 1 and 10 bar (100 and 1,000 kPa) under constant load conditions with incremental (step) loading. The crack length during the tests was monitored by direct current potential drop, which was helpful for defining the applied K corresponding to the onset of subcritical crack growth (KIEAC). Additionally, fractographic analysis of KEAC specimens and results from the fracture toughness evaluation of this material in air at room temperature have also been reported.

ProCrackPlast: a finite element tool to simulate 3D fatigue crack growth under large plastic deformations

Many structural components and devices in combustion and automotive engineering undergo highly intensive cyclic thermal and mechanical loading during their operation, which leads to low cycle (LCF) or thermomechanical (TMF) fatigue crack growth. This behavior is often characterized by large scale plastic deformations and creep around the crack, so that concepts of linear-elastic fracture mechanics fail. The finite element software ProCrackPlast has been developed at TU Bergakademie Freiberg for the automated simulation of fatigue crack growth in arbitrarily loaded three-dimensional components with large scale plastic deformations, in particular under cyclic thermomechanical loading. ProCrackPlast consists of a bundle of Python routines, which manage finite element pre-processing, crack analysis, and post-processing in combination with the commercial software Abaqus . ProCrackPlast is based on a crack growth procedure which adaptively updates the crack size in finite increments. Crack growth is controlled by the cyclic crack tip opening displacement varDelta CTOD, which is considered as the appropriate fracture-mechanical parameter in case of large scale yielding. The three-dimensional varDelta CTOD concept and its effective numerical calculation by means of special crack-tip elements are introduced at first. Next, the program structure, the underlying numerical algorithms and calculation schemes of ProCrackPlast are outlined in detail, which capture the plastic deformation history along with the moving crack. In all simulations, a viscoplastic cyclic material law is used within a large strain setting. The numerical performance of this software is studied for a single edge notch tension (SENT) specimen under isothermal cyclic loading and compared to common finite element techniques for fatigue crack simulation. The capability of this software is featured in two application examples showing crack growth under mixed-mode LCF and TMF in a typical austenite cast steel, Ni-Resist. In combination with a crack growth law identified in terms of varDelta CTOD for a specific material, the tool ProCrackPlast is able to predict the crack evolution in a 3D component for a given thermomechanical loading scenario.

Experimental evaluation of J-integral in elastic and elastic–plastic polymers by means of digital image correlation and higher-order eigenfields under mode-I

This study examines the capability of the digital image correlation method to determine the J-integral for polymers with elastic and elastic–plastic behavior. To achieve this, the required analytical concepts are discussed in detail and single-edge notch tension specimens manufactured out of PMMA and HDPE are tested under pure mode I loading conditions. Three specimens of each material are tested under different loads, and the displacement field at the surface of each specimen is obtained using DIC. Using the least square method, the displacement field derived by DIC is used to determine the higher-order singular and non-singular terms of the Williams expansion. The J-integral for each specimen is then computed by combining these terms. In addition, the J-integral obtained by DIC is compared to that derived by finite element analysis, and an excellent correlation is observed. Lastly, the influence of different DIC parameters on the computed results is discussed.

Multi-parameter identification of the single edge notched tensile specimen using the virtual fields method

The elastic constants are significant indicators to evaluate the damage status during fatigue, whereas the stress intensity factors (SIFs) are essential parameters to study the fatigue crack growth rate. However, due to different configurations of the specimens, tests on these two types of parameters are typically performed independently. To simultaneously characterize the elastic constants and SIFs through a single experiment, the virtual fields method (VFM) for single edge notched tension (SENT) specimens was developed in this study. The proposed approach combines the full-field measurements and virtual fields generated by the finite element method (FEM), which can automatically satisfy the complex boundary conditions and effectively minimize the influence of the plastic zone near the crack tip. The feasibility of this approach was verified by simulation experiments and several key factors involving identification accuracy were investigated. In the application, the SENT testing of Ni-based superalloys was implemented by the digital image correlation (DIC) technique, and the identification results were compared with FEM, the least-squares method (LSM), and theoretical values. The results of the current study demonstrate the excellent accuracy and robustness of this approach, indicating its broad application in the engineering field.

Computational Technique for Crack Propagation Simulation in Viscoelastic Solid Propellant

To further investigate the fracture response in propellant grain, numerical methodology is proposed to cope with crack propagation simulation especially for the mixed mode condition. The numerical discrete scheme of the propellant linear viscoelastic constitutive model is proposed, which provides a key means for the simulation of crack propagation. In order to simulate the cohesive traction distribution on the new crack surface, the extrinsic Park-Paulino-Roesler (PPR) cohesive zone model (CZM) is introduced. To let the crack propagate along any direction determined, element splitting technique and its corresponding topological operations are proposed step by step. Then, computational simulation implementation process is explained in greater detail. Typical fracture problem, single edge-notched tension test (SENT) is solved to demonstrate the efficiency and accuracy of the proposed method. In addition, double edge-notched tension test (DENT) as well as plate tension test with a slant crack is conducted to show the special fracture characters in viscoelastic solid propellant, like time dependence. Computational results reveal that the method proposed can be utilized in further fracture investigation in solid propellant combined with the experimental findings.

Numerical calculation of [formula omitted] to simulate fatigue crack growth under large scale viscoplastic deformations

Crack propagation under low cycle fatigue and thermomechanical fatigue is characterized by high plastic and creep strains that extend over large regions around the crack, so that concepts of linear-elastic fracture mechanics cannot be applied. In these cases, the cyclic crack tip opening displacement ΔCTOD is a promising loading parameter to quantify crack growth. In this work, suitable definitions and Finite Element techniques are investigated and compared for an accurate calculation of ΔCTOD under cyclic mechanical and/or thermal loading. A viscoplastic temperature dependent material model of Chaboche-type is used along with large strain settings, specified for the austenitic cast iron Ni-resist. Extensive two-dimensional analyses of Single Edge Notch Tension specimens revealed that collapsed special crack tip elements are superior compared with commonly used regular quadrilateral 8-node elements. At the same level of accuracy of ΔCTOD, they require an about ten times coarser mesh and show less sensitivity w.r.t. element size for both stationary and propagating cracks. In order to simulate fatigue crack growth, an efficient, fully automated FE-technique is developed for an incremental crack propagation by successive remeshing, whereby the deformations and internal state variables are mapped from the old mesh onto the new one. Recommendations are made regarding important numerical control parameters like optimal size of crack tip elements, length of crack growth increment in relation to plastic zone size and ΔCTOD value.

Crack propagation velocity and fracture toughness of hydroxyl-terminated polybutadiene propellants with consideration of a thermo-viscoelastic constitutive model: Experimental and numerical study

Solid rocket motors are subject to numerous temperature loads during their service life, so it is essential to investigate the sensitivity of propellant mechanical properties to temperature, particularly fracture properties. This paper presents fracture characteristics of hydroxyl-terminated polybutadiene (HTPB) propellant with mechanical-thermal coupled responses. This work investigated the fracture morphology of the HTPB propellant at different temperatures (233.15 K–333.15 K) using a self-developed thermostatic in-situ video imaging. The crack propagation velocity and J-integral were measured using single-edge notched tension (SENT) specimens. In the numerical study, a thermo-viscoelastic constitutive model combined with 1/r singular elements was used to perform calculations on J-integral. The thermo-viscoelastic constitutive model combined with a cohesive zone model was used to simulate crack propagation; meanwhile, load–displacement curves and crack propagation velocity were obtained. All simulation results were analyzed in comparison to the experimental results. The results revealed that temperature could significantly affect the fracture properties of the HTPB propellant. The fracture morphology of the HTPB propellant changed significantly at different temperatures. As the temperature decreases, the strength of the material gradually increases, with a consequent increase in the critical J-integral and a decrease in the average crack propagation velocity. The time ratio governed the regularity of average instantaneous crack propagation velocity with temperature. Furthermore, three simulation methods for calculating the J-integral were analyzed and discussed.

Load transfer between permanent and dynamic networks due to stress gradients in nonlinear viscoelastic hydrogels

Relaxation experiments are performed on single edge notch tension (SENT) and T shape specimens consisting of different variations of polyampholyte (PA) hydrogels. These specimens share a common feature of containing regions of high and low stress/strain. This feature enables us to probe the load transfer mechanisms between permanent and dynamic networks of different strengths. This load transfer mechanism is connected to viscoelastic behavior. PA gels are nonlinear viscoelastic, with time-dependent behavior controlled by the breaking and reforming of ionic bonds in the dynamic network. In contrast to the prediction of linear viscoelastic theory, the displacement and strain fields during stress relaxation are not fixed but change with time in a complex way depending on the strength of the dynamic bonds and the observation time window. These experimental results are explained by a nonlinear viscoelastic model. Additional physical insights are gained by appealing to the nonlinear rheology of dynamic bonds or stickers. Our result shows that load transfer between networks can be controlled by modifying the strength of dynamic bonds.