J-integral Values Research Articles

On the relation between entropy and crack driving force

The concept of debonding entropy provides insight into the physical mechanisms of fracture. It sheds light on how the fracture phenomenon is more intimately related to degradation and entropy. This paper aims to investigate the relationships between debonding entropy and fundamental concepts in fracture mechanics. A direct, simple relationship between debonding entropy and the J-integral value at fracture is developed and validated. The validation of this relation displays the connection between fracture mechanics and entropic degradation.

Effect of repair patch nature on J-integral reduction in notched plates

PurposeThe purpose of this research is to evaluate the effectiveness of different repair patch materials in reducing the stresses at the crack tip of a 2024-T3 aluminum plate. This involves a numerical analysis using the finite element method (FEM) to estimate the reduction in the J-integral value, with the goal of identifying how various parameters related to the patch materials, adhesive properties and loading conditions influence the structural integrity of the repaired plate.Design/methodology/approachThe methodology of this research involves conducting a numerical analysis using the FEM to estimate the reduction in the J-integral value at the crack tip of a 2024-T3 aluminum plate. Three types of patches – metal, composite and functionally graded material (FGM) – were examined under tensile loading conditions, and Adekit-A140 adhesive was used to bond these repair patches to the aluminum plate.FindingsThe analysis considered various parameters, including crack length, the nature of fibers in the composite material, the gradation exponent for FGM patches and the nature of the face in contact with the adhesive for the FGM patch. Additionally, stress analysis was conducted, examining the J-integral values for the plate, shear stress in the adhesive layer and peel stress in the composite patch. The findings highlight that modifying the nature of the repair patch used can significantly enhance the structural integrity of the repaired plate.Originality/valueThe study analyzed J-integral values, shear stress in the adhesive and peel stress in the composite patch. Various parameters, including crack length, fiber type, gradation exponent and adhesive contact face nature, were considered. Results demonstrate that the J-integral value can be significantly reduced by altering the repair patch type, highlighting the effectiveness of customized patch materials in enhancing structural integrity.

Mixed-mode fracture assessment of largely deformable hyperelastic materials highlighting crack removal phenomenon

Due to the special mechanical characteristics, rubbers are nowadays utilized in various industries. In this research, the effect of an existing crack on the behavior of Nitrile Butadiene Rubber (NBR) filled with Carbon Black (CB), which has shown high deformability, is investigated experimentally, numerically and analytically under mixed-mode (I/II) loading. It is observed experimentally that in the cracked largely deformable rubbers, after the initial crack blunting, the crack is nearly removed and the specimen is deformed in such a way that almost no sign of stress concentration factor exists in the sample. Thus, the rupture of these rubbers is divided into two separate phases; named here as the crack removal phase and the final rupture phase, and for each separate phase, a distinct criterion is developed to assess the fracture of cracked rubbers. The good agreement between the theoretical predictions based on each criterion and the corresponding experimental data confirms the very good accuracy of the presented criteria. The independence of critical J-integral value (Jc) from the mode mixity is also investigated.

Simulation of Stress Intensity Factor and J-Integral on UIC 54 Railway Failure Using A Fracture Mechanics Approach

Repeated loading on the railroad tracks will result in fatigue failure. Fatigue failure combined with a defect in the form of a crack in the railroad track will result in a decrease in strength. Defects in the form of cracks are formed due to improper manufacturing and treatment processes. One treatment that can cause the formation of defects in the form of cracks is thermite welding. Improper and non-standard thermite welding techniques can trigger the formation of defects in the form of cracks in the railroad joints. Based on these problems, this simulation aims to obtain information about the value of maximum stress, SIF, J-Intergal, number of cycles, and crack extension from variations in crack size to repeated loading. The method consists of preprocessing, processing and postprocessing. Preprocessing begins with the design of the UIC 54 railroad crack which consists of 3 variations of crack length, namely 10 mm, 15 mm, and 20 mm. The design was tested through static structural simulation using the ANSYS 2021 R2 application. Meshing is configured using an element size of 5 mm and uses curvature capture. The results of the simulation obtained maximum stress values, SIF, J-Integral, number of cycles, and crack extension. Based on the simulation of SIF 1 and J-Integral values on the specimen design with a crack length of 10 mm it shows 362.03 Mpa.mm1/2 of 0.5708 mJ/mm2, for an initial crack length of 15 mm that is equal to 482.81 Mpa.mm1/2 and 0.91738 mJ/mm2, and for an initial crack length of 20 mm, it is 600.54 Mpa.mm1/2 and 1.4465 mJ/mm2. The results show that the increase in SIF 1 and J-Integral will be proportional to the increase in the initial crack length value. .

A digital twin approach toward unlocking elasto-plastic fatigue crack growth rates under negative load ratios

This paper introduces a novel digital twin solution for unlocking the elasto-plastic fatigue crack growth within an S550 steel under negative load ratios. The digital twin transforms solely strain data from a strain-interfaced welded plate joint specimen to the load–displacement curve to compute cyclic J-integral values using the η approach, eliminating the need for load and displacement measurements. The accurate computation of the elasto-plastic ΔJ effectively extends the fatigue crack growth relationship derived from standard fracture specimens. The extended fatigue crack growth relationship accurately predicts the fatigue life of specimens under separate step-up and step-down variable amplitude loading regimes.

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.

Using J-integral analysis to predict the failure of HDPE pipes under crack face load and internal pressure

Cracks in pipes used for water transfer have been identified as a significant contributor to water loss and potential failures. To assess fracture behavior, the J-integral was computed for 3D finite element HDPE pipes (DN 355) with axial internal and external cracks (with a/ c and a/ t ratios of 0.5) subjected to a range of internal pressure (16–30 bar) and crack face load condition. Four ratios of a/ c ranging from 0.3 to 0.9 (with an increment of 0.2) were examined with the internal crack. Results indicate that under face crack loading, the external axial crack exhibits a higher J-integral intensity than the internal axial crack. J-integral values greater than 8.4 kJ/m2 were found to lead to pipe failure, with higher internal pressures (25–30 bar for external crack, and 30 bar for internal pressure). Moreover, the a/ c ratio plays a significant role in influencing the distribution of J-integral along internal crack arc length. For pipes of DN 355 size with axial cracks, internal pressure exceeding 20 bar is not recommended. These findings underscore the importance of considering J-integral values in pipe design to prevent failure.

A study of ductile crack corrections for elastic-plastic fracture toughness tests

This paper critically examines existing ductile crack growth (DCG) corrections for J-integral values calculated with the multi-specimen and elastic compliance approaches, as well as two novel/alternative DCG corrections. The benchmark is represented by the incremental DCG correction prescribed by ASTM E1820-23a for Elastic Compliance tests. Considering calculations performed at both end-of-test and intermediate conditions, most of the existing and proposed approaches tend to under-correct J values, by an amount proportional to the percent of initial cracked ligament. For one of the proposed novel approaches (Pseudo-Resistance Curve Procedure), a tendency to overcorrection was observed. Nevertheless, when values of critical toughness (JQ, JIc) and ductile crack resistance (expressed in terms of tearing modulus, TM) are considered, differences are smaller than the typical uncertainties associated with elastic–plastic fracture toughness test results. Therefore, it does not appear necessary to modify the DCG corrections currently prescribed in the two most widely used fracture toughness test standards (ASTM E1820 and ISO 12135).

Deformation and failure behavior of nanocrystalline WCu

The technical potential of WCu alloys is limited by the modest fracture characteristics of the material system in its coarse-grained condition. To provide a nanocrystalline microstructure and improve mechanical properties, a W-50 at.% Cu composite was processed using high-pressure torsion deformation at a temperature of 200 °C. Therefore, two specimens were subjected to 100% and 1000% shear strains, respectively. Scanning electron and scanning transmission electron microscopy, including nanoscale energy dispersive X-ray spectroscopy mappings, were used to quantify the resulting microstructures. The average grain sizes for the 100% and 1000% deformed specimens were determined to be 14.7 ± 6.6 nm and 10.5 ± 5.6 nm, with the amount of mechanically intermixed W in the Cu grains increasing from 15.4 at.% to 15.9 at.%. X-ray diffraction and selected area electron diffraction studies both revealed strained lattice parameters of the W and Cu phases, respectively. Mechanical properties were investigated using in-situ notched microcantilever tests. The mean conditional fracture toughness and J-integral values were comparable for both conditions, at 3.7 ± 0.4 MPa√m and 245 ± 58 J/m2, respectively. The related behavior could be attributed to the low fault tolerance of the highly deformed states and was substantiated by cleaved globular W grains along the fractured surfaces. In addition, the detailed relationship between the altered grain boundary conditions, the degree of mechanical intermixing and the influence of the different microstructures on the fracture properties were carefully evaluated and discussed to pave the way for future application of these high-strength nanocomposites.

Elucidating the extreme anisotropy in the J-integral value of commercially pure titanium

Extensive multivariant twinning and higher GND-density in TD-RD than RD-ND orientation cause extreme J-integral anisotropy in CP-Ti. Furthermore, c-axis nearly parallel to crack propagation exhibits dominating fluted voids by extensive prismatic slip, while c-axis perpendicular to crack propagation shows flat and fluted voids by dominating multivariant twinning and slip in determining CP-Ti fracture toughness.

The essential work of fracture in peridynamics

In this work, the essential work of fracture (EWF) method is introduced for a peridynamic (PD) material model to characterize fracture toughness of ductile materials. First, an analytical derivation for the path-independence of the PD J-integral is provided. Thereafter, the classical J-integral and PD J-integral are computed on a number of analytical crack problems, for subsequent investigation on how it performs under large scale yielding of thin sheets. To represent a highly nonlinear elastic behavior, a new adaptive bond stiffness calibration and a modified bond-damage model with gradual softening are proposed. The model is employed for two different materials: a lower-ductility bainitic-martensitic steel and a higher-ductility bainitic steel. Up to the start of the softening phase, the PD model recovers the experimentally obtained stress–strain response of both materials. Due to the high failure sensitivity on the presence of defects for the lower-ductility material, the PD model could not recover the experimentally obtained EWF values. For the higher-ductility bainitic material, the PD model was able to match very well the experimentally obtained EWF values. Moreover, the J-integral value obtained from the PD model, at the absolute maximum specimen load, matched the corresponding EWF value.

Numerical simulation of crack in a residual stress field

Fracture mechanics analysis of metallic material is unequivocally one of the principal areas in the study of the failure of materials. The effect of residual stress on failure is often overlooked and usually not considered during the design stage. However, residual stress plays a crucial role in determining the failure of materials. This work studies the behaviour of a crack in a residual stress field. A residual stress field in a welded plate is obtained by finite element simulation of fusion welding. Subsequently, a stationary crack is introduced in the welded plate. J-integral is used to characterize the crack behaviour. The variation in J-integral values with the welding residual stress is studied. It is observed that crack behaviour and stress distribution in a residual stress field depend on the magnitude of primary stress in the material.

Outstanding fracture toughness combines gigapascal yield strength in an N-doped heterostructured medium-entropy alloy

The superior strength and toughness balance prevails in the face-centered-cubic-structured high/medium-entropy alloys (H/MEAs) of low strength, while a gain in yield strength is normally accompanied by a sacrifice in toughness, leading to the strength and toughness trade-off particularly when yield strength increases to the gigapascal levels. Here, we showed the superior fracture toughness by heterostructuring an N-doped CrCoNi MEA having different levels of yield strength higher than 1 GPa. The fracture toughness was 91 MPa·m1/2 at yield strength of 1.3 GPa in the heterogeneous lamella structure and 168 MPa·m1/2 at yield strength of 1.0 GPa in the heterogeneous grain structure. The fracture toughness was attributed to forest hardening plus an extra hetero-deformation induced hardening. The pile-ups of geometrically necessary dislocations were observed to be formed at the domain boundaries to accommodate strain gradient at the plastic zone of the crack tip. The chemical short-range orders were found for the enhanced strain hardening near the crack tip by the interaction with dislocations. Moreover, a new parameter was proposed to characterize the work hardening capacity at the crack tip by the integral of hardness increment in the plastic zone which shows a linear relation-ship with the J-integral value during the crack initiation.

An investigation of the validity of LEFM at the nanoscale in amorphous materials using the atomistic J-integral including entropic effect

The objective of this paper is threefold: (a) to determine the validity of applying the continuum-based linear elastic fracture mechanics (LEFM) to investigate fracture processes at the discrete atomic level in amorphous materials, such as polymers, (b) to quantify the contribution from entropic effects to the J-integral at the nanoscale due to the thermal motion of atoms, and (c) to demonstrate that the atomistic J-integral can be applied to extract the cohesive traction-separation law at a nanoscale notch-tip as a material property in a polymer when specific modeling criteria are obeyed. Verification of the atomistic J-integral algorithm was performed using toughness data for a monocrystalline graphene sheet, before application to a polymer. A generic epoxy polymer (EPON 862-DETDA) was selected for this study, and the simulations were carried out using molecular dynamics (MD). Furthermore, atomistic J-integral was employed as a nanoscale fracture metric to explore flaw tolerance at the nanoscale and to build a methodology to evaluate and predict the material’s initiation fracture toughness. For this purpose, three MD models of edge-notched specimens that are geometrically similar to the ASTM standard compact tension (CT) specimens were developed, each with a different nano-size notch length to study the effect of notch size on toughness and strength. Significant deviation of peak atomistic J-integral values from LEFM-based macro-scale fracture toughness values for epoxy was observed at notch lengths below a critical threshold crack length, indicating that LEFM is not applicable below this length scale. Entropic effects arise in materials at the micro/nano scale due to the random thermal motion of atoms and molecules, especially near crack faces. Results from our MD simulations demonstrated a significant entropic contribution to the atomistic J-integral, especially at elevated temperatures. Notch-size independence of the cohesive traction-separation law near a nanoscale subcritical notch and the effect of temperature were also demonstrated using the atomistic J-integral.

Role of Metastable Austenite on Crack Resistance of Quenching and Partitioning Sheet Steels

The controversial phase, metastable austenite, is deliberately retained in advanced quenching and partitioning (Q&P) sheet steels. Superficially, the plasticity of Q&P steels is enhanced through the transformation induced plasticity (TRIP) effect to a large extent. However, the role of retained austenite on the crack resistance of Q&P sheet steels is ambiguous to date. Tension of double edge notched (DEN) specimens, with different notch radii, was conducted to investigate the role of retained austenite on crack resistance. The fracture toughness of Q&P steels, critical J-integral values Jc, were 402.97 kJ·m−2 (notch radius = 0.18 mm) and 584.11 kJ·m−2 (notch radius = 1 mm). The increase rate in the plastic deformation zone (PDZ) at notch ahead modeled by finite element (FE) methods dramatically decreased with the notch root radius ρ. It reflects a relatively high sensitivity of notch ductility of Q&P steels in relation to notch radius. Propagating microcracks, regularly initiated at phase boundaries in Q&P steels, were found to be effectively impeded by adjacent retained austenite through energy absorption in the form of strain induced martensite transformation (SIMT).

Crack-parallel stress effect on fracture energy of plastic hardening polycrystalline metal identified from gap test scaling

The gap test is a new type of fracture test developed in 2020, in which the end supports of a notched beam are installed with gaps that close only after the elasto-plastic pads next to notch introduce a desired constant crack-parallel compression σxx (also called the T-stress). The test uses the size effect method to identify how such a compression alters the material fracture energy, Gf, and the characteristic size cf of the fracture process zone (FPZ). In 2020, experiments showed that a moderate σxx doubled the Gf of a quasibrittle material (concrete) and a high σxx reduced its Gf to almost zero. A preliminary study by Nguyen et al. (2021) showed that the gap test can be extended to plastic-hardening polycrystalline metals. A generalized scaling law with an intermediate asymptote for large-scale yielding in small structures was derived, and limited tests of aluminum alloy showed its applicability. In this study, geometrically scaled gap tests of notched three-point bend fracture specimens of aluminum are conducted at three different levels of σxx. An extended structural strength scaling law that captures the transition from the micrometer-scale FPZ through millimeter-scale yielding zone (YZ) to large-scale structures which follow linear elastic fracture mechanics (LEFM) is derived and then applied to analyze the effect of σxx. Presented here are the gap tests of aluminum alloy, in which three different levels of σxx are applied to scaled notched four-point-bend beams of depths D = 12, 24, 48 and 96 mm. Using an extended size effect law for plastic-hardening metals, it is found that, at crack-parallel stress σxx≈−40% of the yield strength, the critical J-integral value gets roughly quadrupled, not only because of the well-known enlargement of the hardening YZ whose width is of millimeter scale, but also because of the increase of the FPZ width of micrometer scale. These results can be reproduced neither by line crack models, including the LEFM, cohesive crack and phase-field models, nor by peridynamic and various nonlocal models that ignore the tensorial nature of the material stress at the crack tip. The crack band models, being able to represent an FPZ of finite width and a YZ whose size evolves depending on σxx, can capture the effect of crack-parallel stresses provided that a realistic 3D tensorial damage constitutive model is used. Here, Bai–Wierzbicki’s model is shown to capture the σxx effect on the Gf and Jcr qualitatively.

Establishment of the Cohesive Law of an Epoxy Adhesive Using the Direct Method and the Effect of the Substrate Material

The direct method was applied to characterize the fracture behavior of a structural adhesive obtaining the cohesive law for Mode I. Additionally, the effect of the substrate material in the results was analyzed. The Double Cantilever Beam (DCB) tests were applied to achieve the fracture toughness in Mode I and the J-integral approach was used to measure the critical energy release rate, JIc . The results were then compared and validated using the Compliance Based Beam Method (CBBM). By differentiation of the J-integral values with respect to the crack tip opening displacement (CTOD), the cohesive law was obtained. Moreover, a numerical validation was performed, by comparing the load-displacement experimental results with the numerical data obtained with the Abaqus software. Furthermore, Digital Image Correlation (DIC) analysis was applied resorting to a Python script aiming to optimize the process. The obtained results indicate that the material substrate does not influence the value of the fracture toughness but could positively influence the precision of the obtained cohesive law. Moreover, it was observed that the direct method could predict the fracture behavior of the epoxy adhesive.

Effect of rubber modification on fracture toughness of epoxy adhesives under mode I and mode II loading

In the present study, the effects of rubber modification on the joint strength and fracture toughness of epoxy adhesives under mode I and II loading were investigated using Arcan-type adhesively bonded joints. The results of the fracture tests under mode I loading revealed the occurrence of stress whitening owing to triaxial tensile stresses near the crack tip. The joint strength and fracture toughness were calculated using the J-integral value, where the adhesive layer was considered as an elastic–plastic material. The crack-growth energy was also calculated using the J-integral value, where the adhesive layer was considered as an elastic material. The results revealed that rubber modification under mode I loading induced an increase in the joint strength, fracture toughness, and crack-growth energy. Rubber modification under mode II loading did not induce stress whitening near the crack tip owing to low triaxial tensile stresses. However, macroscopic void growth and significant plastic deformation were observed in the adhesive layer. Rubber modification induced a slight decrease in the joint strength; however, it induced a significant increase in the fracture toughness owing to the growth of the plastic zone in the adhesive layer. The calculated crack-growth energy decreased slightly, in accordance with the joint strength. It was concluded that rubber modification contributed to an increase in the crack-growth resistance under mode I loading and not under mode II loading. Furthermore, a correlation was observed between the joint strength and crack-growth energy.

INTEGRITY ASSESSMENT OF AN AIRCRAFT CYLINDER ASSEMBLY WITH A CRACK

The repeatability of the air-cooled piston engine cylinder assembly failure due to a crack in the cylinder head, as well as its severity from the aspect of crew and passenger safety were the main motives for our research. In this paper an integrity assessment of a cylinder assembly with a crack was performed. By modeling cracks of different lengths in the cylinder head and considering the values of stress intensity factors and J-integral values at a given crack length on the one hand and determining the critical values of these fracture mechanics parameters on the other hand, the stability of the crack was examined. As part of the research, the dependence of the crack length on the stress intensity factor was established. The methodology proposed in this paper can be adapted to assess the integrity of other similar structural elements.

Numerical Analysis of Fracture Failure Behavior of Refractory Lining in Coal-Water Slurry Gasifier.

Fatigue crack fracture is one of the main reasons for the failure of a refractory lining in a coal-water slurry gasifier. To explore the fracture failure behavior of a refractory lining during the operation of a gasifier, the stress intensity factor (SIF) and J-integral at crack front were calculated by the finite element method, and a crack growth model for the refractory was established. At the same time, the effects of different crack length, depth, and angle on the stress and SIF, as well as J-integral distribution around the crack-tip, were presented. The simulation results demonstrated that very large stresses occurring at the crack tip and the distribution regulation of KI and J-integral along the crack front for surface cracks were similar. The maximum values occurred near the two ends of the crack (θ = 0°, 180°), and the minimum values appeared near the deepest crack front (θ = 90°). KI and J-integral values at the same position increase with increasing crack length and depth and decrease with the angle of crack when the a/c was kept constant. Furthermore, J-integral results indicated that excessive crack depths were likely to cause destabilizing crack growth. These results have provided a reliable theoretical basis for fracture analysis and life prediction of the refractory lining in a gasifier.