Crack Tip Opening Displacement Research Articles

Effect of loading rate on mode I fracture behavior of red sandstone: Insights from AE and DIC techniques

The loading rate is an essential factor that influences the fracture characteristics and behavior of rock materials. In the study, a series of mode I fracture tests were performed on semi-circular bending (SCB) specimens of red sandstone under a range of static loading rates (0.005 mm/min–2 mm/min). The results showed that fracture toughness increases linearly with the logarithm of loading rates but the critical crack mouth opening displacement (CMODc) almost keeps constant. The fracture processes of rock were monitored using the acoustic emission (AE) and digital image correlation (DIC) techniques. The accumulated ringing counts increases with the loading rates at a natural logarithm relationship. The quantitative analysis for RA-AF data reveals that the contribution of shear cracks to mode I fracture increases with the loading rates. Prior to the DIC analysis, the DIC parameters were firstly calibrated by comparing the CMOD obtained from the clip gauge with that from the DIC data. By virtue of the strain and displacement fields, the fracture process, including post-peak fracture behavior, was analyzed using the cohesion zone model (CZM) in detail. Some fracture parameters, such as fracture process zone (FPZ) length and width, critical crack tip opening displacement (CTODc) were identified. The results indicate that FPZ length decreases with the loading rates but FPZ width and CTODc are nearly unaffected. The FPZ length at post-peak stage is lower than that at peak, regardless of the loading rate. Finally, the FPZ length measured by DIC is compared to that estimated by five theoretical models. The results show that the FPZ length calculated by the modified Irwin model is very closed to that from DIC.

Stress Intensity Factor of E-Glass Fiber Reinforced Polyester Composites

In order to analyze the stress concentration impact, intensity close to the zone of the crack tip, this work examines the in-plane SIF(SIF) of composite plates utilizing measured crack tip opening displacement (CTOD). The test specimens' E-glass fiber mats were arranged in various ply configurations. The ASTM standards utilized for researching mode I fracture of composite materials served as the foundation for the compact tension (CT) specimen. The mode I, KI Stress intensity factor (SIF), and critical stress, c, were calculated for each specimen along the fracture length propagation based on the experiments. It was found that the SIF is directly proportional with fracture length, or a/W, for all E-glass fiber laminate cases tested. The KIC is often higher in thinner laminates. The presence of woven roving increases the SIF and hence the toughness of the laminate.

Crack-Tip Opening Displacement of Girth Welds in a Lean X70 Pipeline Steel.

Crack-tip opening displacement (CTOD) tests were conducted on girth welds of two API 5L X70 pipeline steels (pipe A and pipe B) to investigate the influence of base metal composition on the fracture toughness of the joint. CTOD measurements across the weld showed that the weld fusion zone had the lowest CTOD values for both pipes, with pipe B having a higher CTOD value than pipe A. Detailed microstructure characterization of the multi-pass weld showed that the fusion zone in both pipes consisted of three distinct zones: the columnar zone, the coarse equiaxed zone, and the fine equiaxed zone. Both the columnar zone and coarse-grained equiaxed zone had acicular ferrite and grain boundary ferrite microstructures, whereas the fine-grained equiaxed zone had a finer ferrite microstructure compared to the other two zones. The main difference between the two pipes was the variation in ferrite grain sizes and the volume fractions of grain boundary ferrite and acicular ferrite. In comparison to pipe B, pipe A, with a higher concentration of Mo, Ni, and Cu in both the base metal and the weld fusion zones, consisted of a higher volume fraction of grain boundary ferrite and a lower volume fraction of acicular ferrite in the columnar and coarse-grained equiaxed zones. The lower concentration of Mo, Ni, and Cu in pipe B likely resulted in the formation of a predominantly acicular ferrite microstructure in the fusion zone, thereby improving the toughness of the weld joint in comparison to pipe A.

Investigation of fracture characteristics of cracked granite suffered from different thermal treatments and water-cooling time

Rock mass may be exposed to high temperature and cooled by water in fire, geothermal resource exploitation and deep underground engineering, which affects the safety of these engineering. In this study, cracked straight through Brazilian disc (CSTBD) specimen was used to study the fracture properties of granite treated with different water-cooling time from 25 °C to 800 °C. A camera was used to record the fracture process of the specimen, the evolution of strain at the specimen surface was obtained by using digital image correlation technology, and the morphological characteristics of fracture surface were observed by using scanning electron microscopy. The results show that water-cooling time has some effects on fracture properties of granite, but its effect is less than the temperature. With the increase of water-cooling time, the mode I fracture toughness decreases first, then increases and finally decreases at the same temperature, and the fracture toughness ranges from 0.419 MPa m1/2 to 0.567 MPa m1/2 at 400 °C. The crack tip opening displacement (CTOD), crack propagation path and fracture surface are related to the energy released during the specimen failure. When the temperature is 25 °C or 200 °C, the energy released is large and the fracture surface is relatively flat with irregular sharp edges, the main cracks are straight lines. At 600 °C, the main crack is zigzag, the CTOD and the maximum principal strain in order can reach 0.143 mm and 0.731 %. This study can help to understand the effect of water-cooling time on engineering rock mass.

Investigating the constraint role in J-CTOD relationship for compact tension (CT) specimen

The Crack Tip Opening Displacement (CTOD or δ) estimation from J-integral (J) defined by ASTM 1820 considers the CTOD dependency on material properties, and the constraint factor (m). The m in Compact Tension (CT) specimen is based on yield to tensile strength ratio (σys/σut) without taking into account of in-plane dimensions as in Single Edge Notch Bending (SENB). Hence, an attempt is made to understand the effect of crack length to specimen width (a/W), specimen thickness to specimen width (B/W) for different σys/σut on CTOD using CT specimen. A new method of estimating the CTOD from FE analysis is demonstrated and validated with 450-intercept method. It has been found that the ASTM 1820 based CTOD (δASTM) assessed values under-estimate the actual CTOD present in the CT specimen. The variation in a/W and B/W doesn’t affect the J-CTOD relationship as stated by ASTM 1820. However, the CTOD measured by FE analysis (δFE) are consistently higher than the δASTM. Therefore, an effort is made to correct the constraint factor, m based on present FE analysis by considering the effect of σys/σut. The proposed corrected constraint factor, mFE, can be employed in fracture applications that generally need both the J-integral and the CTOD.

An Overview of the mechanism-based thermomechanical fatigue method (DTMF) in the design of automotive components

The DTMF damage Parameter described in the paper is the generalization of the creep fatigue parameter (DCF) proposed by Riedel, which quantifies the amount of damage produced by a non-isothermal loading cycle. The entire design methodology is outlined in the text, starting with the calibration of Chaboche's viscoplastic model and then the determination of the thermomechanical fatigue (TMF) parameters. Chaboche is generally a good choice for its ability to describe well both kinematic and isotropic hardening behaviors, also enabling stress relaxation and strain rate dependency to be considered. The DTMF method is based on the fracture mechanics concept of cyclic crack tip opening displacement (ΔCTOD) where the effective stress range takes the crack closure effect into account. This method is typically used to describe the thermomechanical low cycle fatigue behavior of cast irons, cast steels, stainless steels, Inconel, HiSiMo and nickel-based alloys. These materials are used in components that need to withstand high temperatures (higher than half of the melting point) in service as exhaust manifolds, cylinder heads, valves, turbochargers and disk brakes. Three failure mechanisms are detailed here: oxidation, creep and fatigue. Oxidation is a complex phenomenon that may occur when the material is hot under tensile in-phase loading or hot under compressive out-of-phase loading. Creep is a time and temperature dependent diffusion process which is incorporated into the DTMF parameter as a multiplicative factor. In this context fatigue life is defined as the number of cycles to propagate an existent microcrack up to an arbitrary size that is defined on a case-by-case basis.

Experimental Study of the Effect of Wire Electrical Discharge Machining on Crack tip Opening Displacement for Compact Tension Specimens of Low Carbon Steel

Fracture mechanics approach is important for all mechanical and civil projects that might involve cracks in metallic materials the purpose of this paper is to determine a crack tip opening displacement fracture toughness experimentally, also study the effect of thickness on CTOD fracture toughness of low carbon steel and study the effect of Wire Electrical Discharge Machine (WEDM) to have a pre-crack, instead of fatigue pre-crack by using a CT specimen of low carbon steel with a thickness of (8,10, and15 mm), a width of 30mm, crack length of 15mm, and pre-crack of 1.3mm for all samples, this dimension according to ASTM-E399-13, by pulling the specimen in a 100 KN universal testing machine at a slow speed rate of 0.5 mm/min, the load applied on the specimen is generally a tension load. The crack tip plastically deforms until a critical point PC at this moment a crack is initiated. The computer-controlled universal testing machine gives the value of the load and the displacement transducer gives a crack mouth opening displacement. Critical crack tip opening displacement CTOD is found with the plastic hinge model (PHM) method. The result showed the stress intensity factor KI increases with increased loading in the elastic region and the thickness effect refers to the effect of the plastic zone at the crack tip on the stress intensity factor, In a thin specimen, a plastic zone is large at the fracture tip leads to a high-stress intensity factor at the fracture tip but in the thick specimen, on the other hand, has a small a plastic zone and a low-stress intensity factor around the crack tip. The fracture toughness is found to increase with an increase in the thickness of specimens.

Effect of cryogenic conditions on the critical crack tip opening displacement for the laminated material AA2519-AA1050-Ti6Al4V-T62

In the case of operating technical objects in conditions that accelerate material wear, it is necessary to adequately protect the object from the aggressive working environment. There are several possibilities, ranging from applying surface coatings (paint, varnish, galvanic layers) to the use of composites. An example of such a material is a composite formed by explosively welded AA2519, AA1050, and Ti6Al4V alloys. Since the described material is relatively new, its mechanical properties are still being determined. Therefore, in this article, the results of research and their analysis regarding the fracture toughness of the described composite in comparison to the fracture toughness of the base materials in the selected range are presented. The main objective of study was to determine the crack tip opening displacement (CTOD) values for the AA2519-AA1050-Ti6Al4V laminated material explosively welded under ambient and cryogenic conditions. The tests were carried out to determine the effect of the aforementioned temperature conditions on selected properties of the tested laminated material. This paper presents the theoretical basis and the adopted testing methodology. The experimental results obtained and their analysis are also presented. Thanks to the analysis, the effect of cryogenic conditions on the value of the crack tip opening displacement was observed. Moreover, the state of knowledge presented in earlier publications on crack tip opening displacement determination for base materials, i.e. AA2519 and Ti6Al4V, has been extended. The paper also presents a CTOD determination procedure for laminated material based on the knowledge on the mechanical properties of the base materials.

Mode I fracture behavior of glass fiber composite-steel bonded interface – Experiments and CZM

Debonding is characterized as the governing failure mode in the innovative wrapped composite joints made with glass fiber composite material wrapped around steel hollow sections without welding. The prerequisite for predicting debonding failure of wrapped composite joints is to obtain fracture behavior of the composite-steel bonded interface. The mode I fracture behavior of the bonded interface was experimentally investigated using glass fiber composite-steel double cantilever beam (DCB) specimens. The crack length a and the crack tip opening displacement (CTOD) during the test were accurately measured by analyzing the digital image correlation (DIC) data while the strain energy release rate (SERR) was calculated through the extended global method (EGM). The cohesive zone modeling (CZM) was utilized in the finite element model with the proposal of a four-linear traction-separation law to simulate the mode I fracture process. An approach is introduced to determine the critical stages of the proposed four-linear cohesive law by combining accurate measurements of crack length a and CTOD, along with SERR values. The validity of the four-linear cohesive law and the introduced approach to determine the critical stages were confirmed by good agreement in both global and local behavior between the testing and the FEA results.

Effects of Grain Boundary Misorientation Angle on the Mechanical Behavior of Al Bicrystals

This research article explores the effect of grain boundary (GB) misorientation on the mechanical behavior of aluminum (Al) bicrystals by means of molecular dynamics (MD) simulations. The effect of GB misorientation on the mechanical properties, fracture resistance, and crack propagation are evaluated under monotonic and cyclic load conditions. The J-integral and the crack tip opening displacement (CTOD) are assessed to establish the effect of the GB misorientation angle on the fracture resistance. The simulations reveal that the misorientation angle plays a significant role in the mechanical response of Al bicrystals. The results also evidence a gradual change in the mechanical behavior from brittle to ductile as the misorientation angle is increased.

Fracture properties evaluation of structural adhesives using the dual actuator test frame and digital image correlation technique

ABSTRACT This paper implements a dual actuator testing protocol to evaluate the fracture behavior of a toughened epoxy adhesive under mode I and mixed mode I+II loading conditions. Digital image correlation is used to monitor crack propagation and assess adherend and adhesive deformations. A good repeatability between the test results is observed for both failure modes (I and I+II). The constitutive law is obtained by evaluating the J-integral while measuring the crack tip opening displacement. Different mixed mode test strategies are developed in this work. First, an actuator load control protocol is implemented so as to propagate the crack under constant mixed mode I+II ratio and evaluate the fracture envelope of the studied adhesive, which turns out to be adequately described by the Gong-Benzeggagh failure criterion. A second strategy is proposed with a variable mixed mode ratio during the experiment for faster investigation. Using this technique, stable fracture energy values are recorded along the crack propagation path, thus leading to very fast and accurate results.

3D-printed highly stretchable curvy sandwich metamaterials with superior fracture resistance and energy absorption

This paper focuses on the potential of curvy mechanical metamaterials to show how topological design can significantly enhance fracture toughness along the in-plane and out-of-plane (through-depth) directions. The conventional re-entrant unit cell is first reformulated by introducing local curvy ligaments and then additively manufactured by three-dimensional (3D) printing to form a center/edge-notch lattice metamaterial. The new conceptual design provides multi-stiffness unit cells, helping to control stress distribution within a structure under tensile load, specifically in the vicinity of the notches where stress concentrations occur. In other words, curvy unit cells are capable of arresting and blunting the notch under tensile loads and toughening the metamaterials. The crack tip opening displacement (CTOD) method calculates the fracture toughness. Not only can the fracture of lattice metamaterials be controlled along the in-plane direction by replacing unit cells in the sensitive parts of the metamaterials, but a new assembly method is also proposed. This offers that different thin plates of metamaterials with different layouts can be sandwiched to control out-of-plane fracture propagation (through-depth propagation of opening mode fracture) for the first time in fracture mechanics. This novel sandwiching method offers a multi-step fracture and significantly improves the fracture behavior of the lattice metamaterials from brittle to ductile by taking advantage of multiple through-thickness thin plates instead of considering one thick specimen. A detailed analysis of the effects of the ligament curvature value on the fracture behavior is presented. The results reveal that the more curvature, the more extension (ductility) will be realized, but too large curvature design can provide lower energy absorption capacity.

Isothermal and thermo-mechanical fatigue-crack-growth analysis of XH73M nickel alloy

In service-power engineering and aviation, gas-turbine engine structures are operated at elevated temperatures and under extensive variable mechanical loading, which is classified as thermomechanical fatigue (TMF). This coupling effect leads to flaw initiation and growth in components fabricated from thermally resistant nickel-based alloys. This paper presents experimental crack-growth data for isothermal pure fatigue, in-phase and out-of-phase TMF conditions. A crack-growth testing method is developed using inductive heating/forced convective cooling and direct crack-tip opening displacement techniques. The crack-growth experimental results are interpreted based on finite element analyses of the stress–strain rate fields at the crack tip under TMF conditions. Therefore, multi-physics numerical calculations are employed for the interaction of the heat loss from magnetic-field eddy currents with forced convective air cooling through a computer fluid dynamics model, which presents a nonuniform mechanical elastic–plastic stress distribution. Consequently, the dependence of the new nonlinear stress intensity factors on the crack length are obtained for each of the isothermal and thermomechanical cyclic deformation conditions. The polycrystalline XH73M nickel-based alloy tests performed show that, from the crack-growth acceleration viewpoint, the following order of arrangement of fatigue fracture diagrams is formed: isothermal pure fatigue, in-phase TMF, out-of-phase TMF, and isothermal pure fatigue at T = 400 °C and T = 23 °C. The differences and corresponding conclusions based on the interpretation of the experimental results of the crack growth rate characteristics at elevated temperatures in terms of elastic and nonlinear fracture resistance parameters are discussed.

Influence of specimen geometry on the energy release rate in concrete

The energy release rate during the crack propagation in concrete was studied using three-point bending (TPB) beams with different geometries. Expressions for determining the energy release rate were established. A total of 44 beams, i.e., TPB specimens with the height of 150 mm and various spans and the same span of 800 m but different heights, named as Series-T and Series-TH, respectively, were tested. The obtained results reveal that (1) with the crack propagation, the energy release rate curves (GR-curves) monotonically increased and convergence to the fracture energy of each specimen, and the average values were 161.136 N/m and 112.343 N/m for Series-T and Series-TH. (2) For Series-T, with increasing the specimen span from 300 mm to 900 mm, the maximum fracture process zone (FPZ) length kept constant of 68.317 mm, and for Series-TH, the result increased by 187.6 % with increasing the specimen height from 100 mm to 300 mm. Moreover, the relative FPZ length was not affected by the spans and depths of the specimens. (3) The evolution of crack tip opening displacement was only affected by the specimen ligament length, i.e. for the same crack extension length, a larger value was noticed for longer ligament length. (4) The stability during crack propagation can be analyzed using GR-curves.

Microstructure, mechanical and fracture properties of friction stir welded 2195 Al-Li alloy joints

The 8 mm-thick 2195 Al-Li alloy joints were achieved by Friction Stir Welding (FSW). The microstructural evolution, temperature-dependent mechanical properties, and fracture properties were studied. The T1, δ′/β′ and θ′ precipitates were observed in the Base Metal (BM) and the Heat Affected Zone (HAZ). Most of the precipitates, except for re-precipitated δ′/β′ phases, were dissolved in the Nugget Zone (NZ). The tensile specimens that failed at cryogenic temperatures (–196 °C) had the maximum Ultimate Tensile Strength (UTS), and the fracture surface showed the inter-granular fracture characteristics. Compared to those at room temperature (25 °C), the decreasing tensile properties at high temperature (180 °C) were related to microstructure and strain hardening effects. The NZ presented the optimal fracture toughness, and the Crack Tip Opening Displacement (CTOD) was mutually dominated by microhardness and grain size. Analysis on Fatigue Crack Growth (FCG) rates indicates that the Thermal-Mechanically Affected Zone (TMAZ) exhibited the most superior fatigue resistance performance at stress intensity range below 17 MPa·m1/2 due to compressive residual stress and the crack closure effect. The fatigue fracture surfaces reveal that the crack propagation zone was characterized by the striations and secondary cracks. Also, inter-granular fracture behavior was responsible for the fastest FCG rates in the NZ.

Effects of Finish Rolling Temperature on the Critical Crack Tip Opening Displacement (CTOD) of Typical 500 MPa Grade Weathering Steel

In this study, the effect of finish rolling temperature on the critical crack tip opening displacement (CTOD) of typical 500 MPa grade weathering steel was elucidated. The microstructures were observed via optical microscope (OM), scanning electron microscope (SEM), transmission electron microscope (TEM), and electron back-scattered diffraction (EBSD). The cryogenic fracture toughness and microstructures of steels were analyzed at different finish rolling temperatures (780–840 °C). The results show that a mixed microstructure, i.e., granular bainitic ferrite (GBF), polygonal ferrite (PF), and martensite/austenite (M/A), constituent was formed in each sample. With the decrease of the finish rolling temperature, the GBF content decreased, PF content increased, and the high angle grain boundary (HAGB) number fraction of the matrix increased. Furthermore, the fraction of M/A constituents was increased with reduced average size. The value of CTOD increased significantly from 0.28 to 1.12 mm as the finish rolling temperature decreased from 840 to 780 °C. Both the decrease of M/A constituents and the increase of HAGB increased the cryogenic (−40 °C) fracture toughness of the typical 500 MPa grade weathering steel.

Experimental and Numerical Fracture Toughness Evaluation of Spiral Seam Weld of API X65 Steel

In this research fracture toughness of spiral seam weld of API X65 is measured through the ASTM E1820 standard recommendations. According to thin-wall pipe of API X65 in this research, specimen sizes could not satisfy the plain strain condition of ASTM E399 therefore, indirect method is accomplished by evaluating the crack tip opening displacement. According to the nature of welding procedure and inhomogeneous probable defects in the different regions of seam weld, δ-R curve with multi-specimen technique of single-edge notched bend (SENB) specimens is applied for test procedure in this research. The measured CTOD and K1C are 0.23 mm and 265 MPam3/2 respectively. Furthermore, Three-dimensional finite element method numerical evaluation of crack propagation with GTN model has been performed. Good agreement with the other researches was observed for CTOD and fracture toughness of tested material. The difference was about 10 percent.

Effect of strain aging on mechanical properties and engineering critical assessment of X80 girth weld metal

Brittle fracture of girth weld metal in high steel grade oil and gas pipelines is the main failure mode of this kind of facilities, which may be related to the strain aging embrittlement of weld metal. To investigate the influence of strain aging on embrittlement mechanism and safety in service, the mechanical properties and engineering critical assessment of X80 girth weld metal was studied. The results demonstrate that strain aging process leads to the increase in dislocation density and low angle grain boundary. After 3 % and 5 % strain aging process, the yield strength increased from the original 565 ± 9 MPa to 675 ± 6 MPa and 754 ± 4 MPa, respectively, and the crack tip opening displacement decreased from 0.22 ± 0.03 mm to 0.11 ± 0.02 mm and 0.06 ± 0.01 mm, respectively. The deterioration of fracture toughness was attributed to the decrease in plastic deformation ability of weld metal, stress concentration at M-A constituent and Cottrell atmosphere. The change of fracture mechanism caused by strain aging increases the risk of brittle fracture of girth weld, which can be assessed by engineering critical assessment.

Computing the stress intensity factor range for fatigue crack growth testing at 20 kHz

AbstractInertia and damping influence the values of the stress intensity factors (SIFs) at high‐frequency loading and they must be included in computations. In the present study, different dynamic simulation procedures were carried out for two types of specimen geometries and the achieved SIF values were compared. Fast computation procedures such as harmonic modal analysis and direct steady‐state analysis were compared to the computationally expensive transient dynamic analysis. Two different methods for calculating the SIF, the J‐integral and the crack tip opening displacement (CTOD) methods, were applied and compared and the results showed a near perfect agreement in calculation of the mode I SIF. The Rayleigh damping model was introduced into the dynamic computation to investigate its effect and the results revealed a clear effect on the SIF at 20 kHz frequency. The fast direct steady‐state analysis showed good agreement to both harmonic modal and transient analysis with the different damping values used and is, after this study, the recommended procedure.

Three-dimensional numerical study of thickness effect on plastic CTOD and monotonic plastic zone in an aluminium CT specimen

This work is a numerical study of CT specimens with straight cracks and different thickness values submitted to different load levels, which aims to analyse the shape and dimension variations of the monotonic yielded area near the crack tip, examining the impact of variables such as load magnitude, thickness of the specimen and position along the crack front. Additionally, it intends to explore the correlation between the size of the monotonic plastic zone and the plastic CTOD (Crack Tip Opening Displacement) to determine if a well-defined relationship exists. Furthermore, the impact of specimen thickness and load level on plastic CTOD will be explored. A complex plastic zone was found along the crack front, with the maximum area positioned at some distance from the crack front. A plane stress scale was determined considering the size of the equivalent bi-dimensional yielded area. When examining the behaviour across the thickness, no conclusive correlation was identified between the plastic CTOD and the monotonic yielded area. This suggests that utilising this parameter may not be appropriate for studies related to fatigue crack growth. However, when considering average values, a good correlation was found. The increase in thickness decreased the plastic CTOD values at the surface, while the interior values were unaffected.