Compact Tension Specimens Research Articles

Low-cycle fatigue crack growth in brittle materials: Adaptive phase-field modeling with variable-node elements

This work presents an adaptive phase field framework for the simulation of crack nucleation and propagation in brittle materials subject to low-cycle loading. We introduce a fatigue history strain parameter within the phase-field framework to capture the fatigue effect. The resulting coupled differential equations are solved using a staggered iteration scheme. In order to improve the computational efficiency of the phase-field model, an adaptive refinement scheme is introduced. This scheme utilizes an artificial threshold that takes into consideration of both phase-field variables and cumulative fatigue history field variables to determine the elements to be refined. The handling of the hanging nodes resulting from mesh refinement is accomplished through the application of the variable-node element technique, offering a flexible and efficient mesh integration technique. We validate our proposed numerical scheme through five representative numerical examples: single-edge cracked specimen, compact tension specimen, double-edge cracked panel, plate with a hole and plate with multi-cracks and hole. The results demonstrate that the adaptive mesh refinement scheme significantly reduces computational costs without compromising the accuracy of the numerical predictions.

Statistical characterization of specimen size and temperature dependence of cleavage fracture toughness of ferritic steels

AbstractBased on the numerical results on the non‐linear correlation between volume of plastic zone and global loading level represented by stress intensity factor, the dependence of cleavage fracture toughness of ferritic steels on specimen size and temperature is evaluated based on an empirical statistical model. The statistical correlation is supported by two sets of toughness data measured from different sized compact tension specimens at different temperatures. To further improve the accuracy of the statistical model, future work is identified to quantify the variation of volume of plastic deformation zone with loading level and measure the average volume for each microcrack at different temperature.

An investigation on fracture toughness predictions from mini-sized uniaxial tensile specimens with global and local approaches

This study provides investigations on whether the fracture toughness can be accurately predicted from mini-sized uniaxial tensile specimens with existing global and local approaches. The critical toughness model, based on classical fracture mechanics, and the energy release rate (ERR) model, based on damage mechanics, were used as the two representative global approaches. While the finite element simulated compact tension (CT) specimen implemented with Gurson-Tvergaard-Needleman model was used as the local approach. Specimen size effect was judged through the viewpoints of stress–strain relationship and damage development. It was proved that the specimen size has no significant influence on stress–strain relationship, and has little influence on damage developments when the thickness reaches 1.0 mm. Fracture toughness predictions were conducted on four metals, including two steels (SA508Gr.3Cl.1 and 18MnMoNbR), one aluminum alloy (6061-T651), and one titanium alloy (TC4). For TC4 exhibiting brittle cleavage features on the fracture surface of CT specimens, neither the global nor the local approach can accurately predict its fracture toughness. For 6061-T651 exhibiting both ductile and brittle features on the fracture surface of CT specimens, there exists significant macroscopic crack propagation at the moment of conventional fracture toughness determination. The existence of significant macroscopic crack is inconsistent with the “equivalent crack” assumption in the ERR model, leading to a failure in its fracture toughness prediction. For two steels following the “equivalent crack” assumption, the ERR model and the local approach yield more accurate predictions (with the maximum error around 10 %) than their critical toughness counterpart (with the maximum error around 30 %).

Role of precipitate-induced [formula omitted] twins on anisotropic fracture behavior in Mg-3Al-0.5Ce alloys

Anisotropic fracture toughness (FT) in a hot-rolled Mg-3Al-0.5Ce magnesium alloy has been investigated using fatigue pre-cracked compact tension (CT) specimens with the notch (an)‖ to the rolling direction (RD) and transverse direction (TD). During testing, notable non-linear load–displacement behavior before peak load indicated significant crack tip plasticity. Thus, elastic–plastic FT (JIC) was evaluated and found to be 20.7N/mm and 15.8N/mm for an‖ to RD and TD, respectively. Long-aligned Al11Ce3 precipitates were present in this alloy within the elongated grain boundaries along RD. During FT testing, profuse 101¯2〈101¯1〉 extension twins (ET) with c-axis almost ‖ and lamellae morphology almost ⊥ to RD formed between these elongated precipitates, irrespective of the notch, an‖ to RD or TD. The ET lamellae ⊥ and ∥ to crack path lead to trans and inter lamellar crack for an‖ to RD and TD, respectively. Translamellar crack in an‖ to RD leads to comparatively high strain hardening, dislocation density, geometrically necessary boundaries, and grain refinement, indicating larger plastic energy dissipation and thereby has higher JIC than in an‖ to TD with interlamellar crack.

Experimental, Analytical, and Computational Studies on the Fatigue Crack Growth Behavior of a Titanium Alloy under Cold-Turbistan Spectrum Loads

Abstract The fatigue crack growth (FCG) behavior of Ti-6Al-4V alloy subjected to spectrum loads was experimentally determined and compared with predicted behavior by analytical and computational methods. In the experimental method, a compact tension (CT) specimen of Ti-6Al-4V was tested under standard cold-Turbistan spectrum loads to determine crack propagation behavior. Spectrum fatigue tests were conducted with triangular waveform at 2 Hz. In the analytical predictive method firstly, constant amplitude FCG tests were conducted at several stress ratios and a unified FCG law based on crack driving force, K* was derived for Ti-6Al-4V alloy. Then, the crack growth for every rainflow-counted fatigue load cycle in the cold-Turbistan sequence was determined using the derived FCG law. In the computational method, a global and a local model of the CT specimen of Ti-6Al-4V were created in HYPERMESH and FRANC3D, respectively. The FCG behavior under the cold-Turbistan spectrum was then predicted using FRANC3D and MSC NASTRAN. The required materials constants for the FCG law in the FRANC3D software were derived from the experimental constant amplitude FCG rate data of Ti-6Al-4V alloy. It was observed that both methods of FCG predictions, i.e., analytical and computational methods, although conservative, compared quite well with experimental results.

Numerical fracture toughness evaluation of SS316L CT specimens using an Elastic Plastic Fracture Mechanics (EPFM) approach

In this study, fracture toughness was determined using an elastic-plastic fracture mechanics approach via numerical simulation. The material chosen for study is austenitic stainless steel 316L, which is extensively used in the nuclear industry for core internal structures. Three different SS316L conditions were considered for the analysis, including welded and post-weld heat-treated conditions aged at 300 °C for 10,000 hours (over-aged) and at 400 °C for 5,000 hours (peak-aged). A compact tension (CT) specimen of standard dimensions, which was taken from ASTM E1820–01, was used to perform the analysis. The J-integral value that is obtained for those three conditions was compared with the base material, which was taken from the open literature. It was found that theJ-integral values of SS 316L for welded conditions were lower than the base material. Also, J-integral values of SS 316L for the two post-weld heat-treated conditions were found to be greater than the weldments but less than the base material. It can also be noted that the values obtained for the SS316L weldments and the post-weld heat-treated sample aged at 335 °C for 10,000 hours were notably similar.

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.

The effect of inclusions and pores on creep crack propagation of linear friction welded joints of GH4169 superalloy

Superalloy has become the key material in components of blisks for aero-engines produced by linear friction welding. However, during the long-term service of the blisks, stress rupture occurs on the blisk under long-term creep. In this study, the linear friction welded joints of GH4169 superalloy were studied with experiments and numerical simulation. The Sin-Hyperbolic creep-damage constitutive model was established. Based on the compact tension specimen model, the numerical simulation of crack propagation was carried out, analyzing the effect of defects in linear friction welded joints such as cracks, inclusions, and pores on creep crack propagation. Results show that inclusions have an impact on the deflection and promotion of creep crack propagation. The maximum values of crack propagation rate can be observed when radius is 0.03 mm for circular inclusions and length-to-diameter ratio is 3 for elliptical inclusions, respectively. When the transverse distance between the center of the pore and the crack tip is 0.6 mm, the effect on crack propagation is the most significant, with the crack deflecting and expanding towards the direction of the pore. The effect of elliptical pores on creep crack propagation is more significant than that of circular pores. When the length-to-diameter ratio is 3, cracks have initiated firstly on both sides of elliptical pores. When the angle between the pore and the prefabricated crack is 0°, the elliptical pore has the greatest deflection effect on the creep crack. Overall, the effect of pores on creep crack propagation is stronger than that of inclusions.

Investigation of Austempering Effect on Fatigue Crack Growth of AISI 4140 Steel

The compact tension (CT) and tensile specimens of the AISI 4140 steel in cold rolling condition (untreated steel) were austempered by immersing it into the salt bath at 362°C for 60 minutes. The tensile strength properties and the fatigue crack growth (FCG) resistance were performed to investigate the effect of the austempering process in AISI 4140 steel. A significant increase in the yield strength for austempered steel is about 8.7 % and the elastic strain energy increases by 55.7 %. Austempered steel's fatigue crack cycle is longer than that of untreated steel. Data of stress intensity factor range (ΔK, MPa.m1/2) and FCG rate (da/dN, m/cycle) was constructed in double log plot x-y axes for determining the materials constants m and C according to Paris’s law equation using a linear regression method. From the curve of ΔK versus da/dN, the constant m value for austempered steel (m = 3.45) shows better resistance than untreated steel (m = 3.77). On the other hand, the constant C value of 1.409×10-12 for austempered steel is one order magnitude higher than that of untreated steel (C = 4.151×10-13). The resistance of austempered steel against fatigue crack growth can be attributed to the formation of a bainite structure.

Study on the multi‐scale online fatigue crack deformation and growth behaviors under overload in Q&P steel

AbstractThe multi‐scale online fatigue crack deformation and growth behaviors under single overload (SOL) and periodic overload (POL) case in Quenching and Partitioning (Q&P) steel were studied using two micro cameras and sub‐image stitching and matching digital image correlation (DIC) method. Firstly, the microscopic crack tip speckle images and crack images on both sides of the compact tension (CT) specimen during the fatigue crack growth (FCG) process were collected under different overload parameters. Then, the FCG overload retardation, crack tip closing and blunting behaviors, and the crack tip strain distribution and evolution, overload retardation mechanism were analyzed. In addition, the corresponding multi‐scale FCG morphological characteristics and material microstructure under overload case were observed. The results indicate that the overload ratio and interval affect the overload retardation effect of Q&P steel seriously; the overload crack tip blunting and plastic zone are the major factors inducing the overload retardation effect in Q&P steel.

Effects of Ion Irradiation on Stage II Fatigue Crack Growth and Plasticity

AbstractFatigue crack growth characteristics of ion irradiated compact tension (CT) specimens were evaluated in the Paris law region. Fatigue crack growth was monitored under tension‐tension loading and the thermoelastic response was measured. Two stages of crack propagation were identified. In the first 300,000 cycles, crack growth rates of irradiated and unirradiated specimens were comparable and plastic zone area was found to be independent of crack length. Beyond 300,000 cycles, irradiated specimens showed a greater crack growth rate; additionally, the plastic zone area increased with crack length. The increase in crack growth rate was attributed to irradiation hardening. The plastic zone area was found to be dependent on the crack path, especially in the initial stages of crack propagation. Local peaks in the value of the area of the plastic zone were found to be associated with greater crack tortuosity and secondary cracks. As a result, decreases in plastic zone area were associated with greater crack growth rates.

Stress Corrosion Cracking of High-Strength Ni-Base Alloys in Pressurized Water Reactor Primary Water Containing KOH vs. LiOH

The stress corrosion cracking (SCC) behavior of high-strength Ni-base Alloys X-750 and 718 has been investigated to assess the effect of replacing LiOH with KOH as the pH moderator in pressurized water reactor (PWR) primary circuit coolant. The SCC initiation behavior of X-750 was evaluated by multitensile specimen constant load test in either LiOH- or KOH-containing PWR primary water. The SCC growth behavior of X-750 and Alloy 718 was evaluated on compact tension specimens with on-the-fly changes between LiOH- and KOH-containing water in three different PWR primary water chemistries. Direct current potential drop technique was used for in situ monitoring of crack initiation time and crack extension in SCC initiation and propagation tests, respectively. The results suggest no significant effect of KOH vs. LiOH on the SCC initiation or propagation of the tested materials.

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.

Effect of cathodic protection on the corrosion fatigue crack growth behavior and fatigue life of XS-grade shipbuilding steel

Shipbuilding steels are subjected to corrosion fatigue damage phenomena due to conjoint effects of cyclic loading by sea waves and corrosive seawater environment, which often leads to premature failure of ship hull structures. In practice, the impressed current cathodic protection (ICCP) technique is applied to mitigate ship hull corrosion by electrochemically making it cathodic. It is implemented by impressing a direct current to minimize the electrode potential to a predefined protection potential. It is significant to study the effect of ICCP on the corrosion fatigue crack growth rate (CFCGR) behavior and fatigue life assessment of ship hull structures. In this study, CFCGR behavior of high-strength XS-grade shipbuilding steel was investigated in unprotected freely corroding (FC) and protected ICCP (at – 800 mV) conditions using compact-tension specimens at 0.1 Hz frequency in artificial seawater (3.5 wt.% NaCl solution). After crack-closure corrections, it was found that the ICCP-protected specimen (∆KTH = 18 MPa √m) exhibited higher sub-critical or threshold corrosion fatigue crack propagation resistance as compared to the FC specimen (∆KTH = 14 MPa √m). Fractography of the FC specimen revealed the debonding of non-metallic inclusions and formation of micro-pits/secondary cracks as dominant damage mechanisms. ICCP-protected specimen exhibited a signature pattern of parallel secondary cracks and a proportional increase in their density with increasing stress intensity levels during primary crack growth. This fracture morphology indicated the primary-crack branching and further arrest, leading to retarded crack growth rates under ICCP-protection. Fatigue life analysis also confirmed this finding, where the beneficial ICCP-protection effect resulted in at least two times enhancement in fatigue lives from the unprotected FC condition.

Application of EMI technique in crack propagation under the block loading conditions for AA6061 alloy

The behaviour of a component under real/random loading conditions can be studied by converting the random load into block load. Therefore, knowledge of the initiation and propagation of a crack under block loading conditions is very important for the safety and reliability of machine components / structures. Electromechanical impedance (EMI) is a real-time damage evaluation technique in which simultaneous use of the high-frequency mechanical excitations and responses of the structure are made by employing a piezoelectric transducer. In the present study, an experimental methodology to monitor fatigue crack initiation and propagation under block loading conditions for AA6061 aluminium alloy has been studied with the help of the EMI technique. The piezoelectric sensor bonded on the Compact Tension (CT) specimen acts as an actuator and sensor both. The conductance signature provided a sufficient information about the damage and crack growth under high low and low high block loading conditions. The conventional crack growth rate versus range of stress intensity factor plot matches well with the crack growth rate versus shift in resonant frequency.

Effect of Temperature and Ageing on Fracture Toughness of Alloy 617M

In recent years, Advanced Ultra Super Critical (AUSC) plants have used Ni-Cr-Co-Mo based alloy 617M for high-temperature components like steam piping and rotors, where material resistance against fracture after prolonged exposure in a hostile environment is a matter of concern to the designers. To this end, fracture toughness characterization of the material in as-received and aged conditions using an elastic-plastic fracture mechanics (J-R curves) approach can provide a significant input towards the component integrity assessments at service conditions. In this study, J-R curves of the alloy 617M have been determined for the as-received and differently aged (up to 20000 h at 710 °C) conditions using compact tension (CT) specimens following ASTM E 1820-13. Repeated tests have been carried out at temperatures 27 °C, 650 °C, 710 °C and 750 °C. The fracture toughness (JIC) thus determined, has shown a declining trend with test temperatures. This attributes to the ease of the crack initiation process owing to the γ′ induced matrix hardening and subsequent ageing-inducing precipitations of M23C6 carbides at the grain boundaries.

Impact of Element Layout and Notching Technique on the Fracture Toughness of FFF-Processed Thermoplastics

This work explores the effects of notching method and element layout on the fracture loading properties of thermoplastic materials processed using fused filament fabrication (FFF). Three common thermoplastic materials were used (acrylonitrile butadiene styrene, polylatide, and polycarbonate). Four different notching methods were used, with printed and machined notches and with and without pre-cracking on ASTM D5045 compact tension specimens (n = 36). It was concluded that the notching method has a statistically significant impact on the sample preparation and that pre-cracking is necessary in all cases. Using this information to prepare specimens, a designed experiment using four different element layout strategies and two different nozzle sizes was completed with a total of 72 tests. The layout pattern was shown to have a very strong effect on the maximum fracture load, with the nozzle size showing a smaller but still statistically significant impact. With the exception of one layout using polycarbonate with likely design-driven printing defects, the results were very consistent through several replications. The results of this study are useful for making design decisions with FFF-processed materials, for better understanding the impact of the process design, and for working toward standardized printing and testing methods for additive manufacturing.

On the determination of the reference temperature T0 of the Master-Curve method using subsized compact tension specimens

Structural integrity of reactor pressure vessel (RPV) is of primary importance to ensure the long-term safety of light water reactors. The pressure vessel made of ferritic steel presents a ductile to brittle transition and experiences neutron embrittlement that needs to be quantified. The so-called Master-Curve (MC) method, standardized in the ASTM-E1921, is commonly used to determine a reference temperature T0, which indexes the median toughness-temperature curve in the transition at 100 MPam1/2 for one inch-thick specimens, referred as 1T-specimen. Since brittle fracture toughness is strongly specimen size and geometry dependent, provisions are given in the ASTM-E1921 standard to take into account this effect. The standard also imposes restrictions on the testing temperature range where the fracture tests have to be performed. In this study, we carried out a series of fracture tests with subsized compact tension small specimens (0.18T) to determine T0. In a first step, we calculated T0 by following all recommendations of the standard strictly to get a valid T0 value. Then, we took in consideration fracture toughness data obtained out of the recommended testing temperature range and showed that a reliable determination of T0 can be done under these circumstances. Statistics show that this approach is quite reliable if more than 10 data are considered.

A nonlinear kinetic rate model for unifying fatigue crack growth rates of nickel-based superalloys at room and elevated temperatures

This study presents a nonlinear kinetic rate model to describe the temperature-dependence of fatigue crack growth rate (FCGR) of nickel-based superalloys across a wide range (20 to 650 °C). FCGR testing was performed using compact tension specimens of GH4742 superalloy. Metallography analysis on crack growth paths of two tested specimens suggests there is a local resistance to pure model I cracking at 20 °C, which can greatly be weakened at 650 °C. Compared to the classical Arrhenius equation, the proposed model captures the nonlinear temperature-dependence, and yields more accurate results by reducing the scatter factor from 5 to 3.

An effective free-meshing and linear Step-Wise procedure to predict crack initiation and propagation

An automated procedure is proposed to calculate fracture initiation and propagation in two-dimensional structures. The application uses and enriches the Hybrid Semi-Analytical Method to calculate mixed-mode stress intensity factors in linear elastic fracture mechanics framework. The strategy does not necessitate prior knowledge of the starting crack tip location within the structure, resulting in suitable for analyzing structures without initial defects. When neither a priori invitation nor pre-existing notch is provided, the fracture initiation is assumed to occur when the structure reaches its elastic limit, and a non-linear analysis is conducted under the prescribed load to identify the first occurrence of permanent strain and to locate where the crack opening occurs. As the crack propagates, solely linear elastic analyses are performed to calculate the stress intensity factors. Relying upon these parameters, the procedure implements an evolutionary algorithm based on a step-by-step evaluation of the crack increment and direction. A global–local energy-based criterion is employed to drive fracture propagation. Neither local refinement nor mapped meshes around the crack tip are required, resulting in a streamlined and efficient free-meshing strategy.The calculation has been implemented in a standard finite element environment, and several numerical examples have been investigated, both from a qualitative and quantitative point of view. Qualitative crack paths have been shown for a square hollow plate under pure tensile and shear loads, and a modified Single Edge Notched specimen in bending, as a function of the mutual void positions, distance from the plate edges, and different notch lengths. Finally, an effective comparison in terms of forces-displacement curves has been presented between the proposed procedure, and a lab test for a modified Compact Tension specimen under tensile loading, demonstrating the overall accuracy and reliability of the presented strategy.It is felt that the proposed procedure could pave the way for designing hollowed structures and investigating the corresponding evolutionary laws that relate structural geometries to the insurgence and spread of fractures, and envisaging crack initiation and propagation within inhomogeneous media.