Critical Stress Intensity Factor Research Articles

Non-equilibrium nature of fracture determines the crack paths

Local kinetic processes during crack growth are non-equilibrium and discrete and thus cannot be resolved in the framework of continuum thermodynamics. Atomistic modeling using existing empirical or machine-learning force fields also fails to offer satisfactory solutions for the lack of sufficient accuracy in predicting the energetics of strong lattice distortion and edge cleavage during fracture. The problem is addressed here by using a high-fidelity neural network-based force field for fracture (NN-F3) that covers the space of strain states up to material failure and the non-equilibrium, intermediate states at the crack tip. Atomistic simulations using NN-F3 reveal spatial complexities from lattice-scale kinks to sample-scale crack patterns in 2D crystals such as graphene, which evolve along the process of crack growth. The non-uniform lattice distortion and undercoordination of cleaved edges at the crack front play critical roles in the fracture process. The fracture toughness by cleaving specific edges thus cannot be quantified by their energy densities with relaxed atomic-level structures, which, however, have been widely used in the literature. Instead, the fracture patterns, the critical stress intensity factors corresponding to the kinking events, and the energy densities of edges in the intermediate, unrelaxed states offer reasonable measures for the fracture resistance and its anisotropy, which can be determined from experimental or simulation data with the atomic-level resolution. The findings conform well with recent experimental observations.

Investigation of Multi-Factor Stress Corrosion Cracking Failure of Safe-End Feedwater Lines of Submarine Power System.

The corrosion process under the complex safe-end feedwater line conditions was investigated via experimental lab testing and numerical simulation. The corrosion of safe-end feedwater lines was controlled through the combination of galvanic corrosion, residual stress, and flow velocity. Firstly, galvanic corrosion occurred once the 20 steel was welded with 316L stainless steel. The pitting corrosion could be observed on the 20 steel side of the weld joint. Secondly, a vortex flow was detected around the welding bump and within the pits. The growth of the pits was accelerated in both the vertical and horizontal directions. Finally, under the residual stress condition, the stress intensity factor (K) at the bottom of the pits was easier to reach than the critical stress intensity factor (KISCC). Then, pitting was transformed into stress corrosion cracking which then propagated along the weld line. Therefore, the critical factor inducing the failure of safe-end feedwater lines was the combined action of galvanic corrosion, residual stress, and flow velocity.

3D-generalized maximum tangential strain criterion for predicting mixed-mode I/II/III fracture initiation of brittle materials considering T-stress effects

To overcome the difficulty of predicting the initiation and conditions of three-dimensional (3D) cracks, we proposed a novel 3D-generalized maximum tangential strain (3D-GMTSN) criterion for mixed-mode I/II/III loading conditions, considering the effects of T-stress and Poisson’s ratio. The proposed strain-based criterion can predict the initiation direction and conditions of cracks under mixed-modes I/II, I/III, II/III, and I/II/III. The criterion was compared with the existing criteria for mixed-modes, and the results were compared with the experimental results. Our study indicated that the criterion considering T-stress effects can predict the crack initiation angles and the critical stress intensity factors (CSIFs) for arbitrary mixed-mode fractures. Specifically, the criterion provides better predictions of the CSIFs under the mode II-dominant conditions. The 3D-GMTSN criterion was better for predicting the out-of-plane crack initiation angles and CSIFs of brittle materials containing mode III cracks as compared to the existing criteria.

Atomistic details of grain, crack, and notch effect on the mechanical behavior and fracture mechanisms of monolayer silicon carbide

Recently, sp2-hybridized single-layer SiC, analogous to graphene, has received much attention in nanoelectronics and nanoelectromechanical systems because of its remarkable thermal, electrical, and mechanical properties. However, the unique properties and related applications strongly depend on the growth of a single-crystal and large-area two-dimensional SiC. The majority of synthesized SiC monolayers exhibit a natural polycrystalline structure, comprising single-crystalline grains with diverse sizes and orientations. Moreover, the emergence of structural defects, including cracks and notches, poses challenges that are difficult to overcome during both the fabrication and subsequent processing stages. In this paper, we explore the atomistic details of grain, crack, and notch effect on the mechanical behaviors and fracture mechanisms of single-layer SiC using molecular dynamics simulations. Increasing grain size from 2 nm to 35 nm gradually increases the elastic modulus and fracture strength, which fits well with the inverse Pseudo Hall-Petch relationship. However, an anomalous trend of decreasing as well as increasing fracture strain is observed with the increasing grain size. For polycrystalline SiC with a 2 nm grain size, the elastic modulus and fracture strength are roughly 87% and 41% of those observed in single-crystalline SiC. Notably, when comparing the impact of rectangular crack and circular notch defects, the circular notch exhibited a more pronounced effect in diminishing mechanical behavior under both armchair and zigzag orientational loading. The circular notch produces considerable amorphization around the notch, but the rectangular crack does not show any significant dislocation or amorphization around the crack. The critical stress intensity factor, energy release rate, radial distribution function, and potential energy per atom are calculated to explain all the fracture properties. The effect of temperature and strain rate is also investigated for all the defect-induced samples. Overall, our results provide new insight and understanding of the mechanical behavior and fracture mechanisms of polycrystalline, crack- and notch-induced SiC, and set a standard for making and designing new nanodevices and nanostructures made of SiC.

Dependence of Critical Stress Intensity Factor on Crack Depth From the Loading Boundary of Crystalline Silicon

Abstract In the present work, an atomistic scale investigation is done on crystalline silicon to understand the effect of crack depth from the loading (pulling) boundary on the critical near-tip state of stress. For various depths of embedded cracks, the near-tip stress field has been calculated at the critical state just before the crack propagation initiation. This atomistically calculated stress field is found to be quite close to those found using continuum linear elasticity. Thereafter, the critical stress intensity factor (SIF) is calculated for all cases by fitting the atomistically calculated normal stress over inverse square-rooted distance from the crack tip. It has been found that the closer the crack is located to the loading boundary (i.e., lesser depth), the lower is the (locally calculated) critical SIF. This implies that it is easier to initiate crack propagation when the crack is located closer to the loading boundary. The claim is also strengthened by a similar observation of (globally calculated) boundary stresses at the critical state just before crack propagation initiation.

Emergence of crack tip plasticity in semi-brittle α-Fe

Fractures in body-centered-cubic metals and alloys below the ductile-to-brittle transition temperature are brittle. This is theoretically explained by the notion that the critical stress intensity factor of a given crack front for brittle fracture is smaller than that for plastic deformation; hence, brittle fracture is selected over plastic deformation. Although this view is true from a macroscopic perspective, such a fracture is always accompanied by small-scale plastic deformation near the crack tip, that is, crack tip plasticity. This paper investigates the origin of this plasticity using atomistic modeling with the machine learning interatomic potential of α-Fe. Some plastic modes are activated by rapid crack propagation, whereas no plasticity is activated when the crack tips are gradually fractured. The group of activated atoms dynamically caused by brittle crack propagation was identified as the precursor of plasticity.

Gray correlation analysis between mechanical performance and pore characteristics of permeable concrete

Pervious concrete is a type of sustainable construction material used in pavement engineering due to its advantages in water permeability, skid resistance, and sound absorption performance. This study investigated the pore characteristics of five types of pervious concrete, along with the uniaxial compression behaviors and semi-circular bending (SCB) fracture performance. The critical stress intensity factor was obtained using the equivalent energy approach. Gray relational analysis was conducted between the mechanical performance and the pore characteristics. Pore indicators include the effective porosity, 2D porosity along the specimen height, 2D coordination number (CN) along the specimen height, 2D pore radius, 2D specific surface area, 3D CN, 3D pore radius, and 3D virtual porosity. Results indicated that from M1 to M3, when cement mortar content decreased from 520 kg/m3 to 408 kg/m3, the effective porosity increased from 18.95% to 27.43%, and the compressive strength and fracture toughness decreased obviously. For the same type of pervious concrete mixture, with the increase of notch length, the critical stress intensity factor decreased accordingly. The 2D porosity distribution, 2D pore size distribution, and 2D CN distribution presented a symmetrical trend of decreasing, then increasing, and then decreasing with the increase of specimen height. Aggregate with the gradation within the range of 9.5 mm to 19.0 mm generated a higher compressive strength, larger effective porosity and larger pore size compared to the gradation of 4.75 mm∼9.5 mm. The results of CN and pore radius generated from the 3D pore network model were larger than the corresponding 2D values. The gray correlation analysis revealed that 2D pore radius and 3D pore radius played critical effects on the uniaxial compressive strength and fracture resistance, while 2D CN and 3D CN were the least significant factors affecting the mechanical performance.

SEI-Coated Carbon Particles: Electrochemomechanical Fracture Mechanisms

By starting from fundamental physical principles, a generalized theoretical framework was developed to engineer the intercalation-induced mechanical degradation in SEI-coated carbon particles from the surrounding electrolyte in rechargeable lithium-ion batteries (LIBs). Six elemental regimes of fracture formation in spherical electrochemically active carbon particles of radius, r p , coated with an SEI layer of thickness, δ ≪ r p , have been identified: The pristine regime, the SEI debonding regime, the SEI surface flaw regime, the surface carbon flaw regime (delithiation), the internal circular carbon flaw regime (lithiation), and the carbon exfoliation regime (lithiation); as well as four combined regimes during delithiation and four combined regimes during lithiation. Results are summarized in terms of C-Rate versus particle size, degradation maps, to identify LIB operation conditions where the performance can be optimized, while suppressing the decrepitation of the SEI-coated carbon particle system. Improved porous electrode layers that deliver longer battery life are possible by selecting electrolytes that considering the design of SEI-coated carbon particles of tailored elastic stiffness and critical stress intensity factor, so that they are safe from developing a chemomechanically induced flaw, exfoliation, or carbon re-forming, during both lithiation or delithiation in the 1 to 10 μm size particle, and C-Rates < 1 C.

Evaluation of the Fracture Strength of Polyester Composite with Pineapple Leaf Fiber Reinforcement

The development of natural fibre composites is needed to replace synthetic composites which are difficult to decompose. However, natural fibre composites have many weaknesses that need to be studied, including being brittle and easily cracked. One of the things carried out in this research is a material derived from unsaturated polyester which is reinforced with natural fibers from pineapple leaves which are used to reduce the percentage of synthetic materials from polyester which can form composites that are easily decomposed. With this research, engineering in the engineering field such as in the field of raw materials for fishing boat bodies, tourist boat bodies, and fishing boats is very helpful. This unsaturated polyester mixture with 20% pineapple leaf fibre has the highest critical stress intensity factor of K_1c= 1.733 MPa.m0.5, an increase from K_1c= 0.779 MPa.m0.5 in pure unsaturated polyester. With the highest performance, this material can withstand good fracture strength, making it good and useful for engineering applications. This research increased the toughness and crack resistance of the UP material treated with the addition of the SN mixture by 222.47%.

Effect of external magnetic field on electric current-induced fracture of notched thin metallic conductors: Part 2- High magnetic fields

In the companion report (Telpande et al., n.d.), we discussed the impact of a weak external magnetic field (up to 0.4 T) on the electric current-induced fracture of pre-notched thin metallic conductors, revealing a linear decrease in critical current density, jc, necessary for crack propagation. This study extends the investigation to explore the effects of stronger external magnetic fields (0.6–1 T) on the fracture of pre-notched, current-carrying metallic foils. The experimental analysis reveals a substantial, albeit linear, drop (up to 40 %) in jc under stronger magnetic fields. Interestingly, calculations of the dynamic stress intensity factor, KIE,t, which assesses the interplay between applied current density and external magnetic field, indicate crack growth under a strong magnetic field even when KIE,t is below the plane stress critical stress intensity factor, KIC. A remarkable phenomenon emerges: the application of electric current pulses combined with strong external magnetic fields induces observable surface undulations near the notch tip. A comprehensive 3D finite element model, integrating linear and nonlinear buckling analyses under multiphysics stimuli, attributes these undulations to localized buckling near the notch tip. This buckling-induced stress redistribution near the crack tip contributes to an overall reduction in fracture toughness due to mode mixity, leading to the fracture of the Al foil below KIC. This investigation, along with the companion report (Telpande et al., n.d.), significantly advances our understanding of the effects of magnetic fields on the fracture of current-carrying conductors.

Experimental analysis of blended nanocomposites processed using compression molded microwave process

Microwave irradiation has emerged as a versatile and efficient method for synthesizing polymer nanocomposites, offering advantages such as selectivity, speed, and effectiveness in heating materials. This study explores the blending of low-density polyethylene (LDPE) and polypropylene (PP) with carbon nanotubes (CNTs) using microwave processing. The nanocomposites were characterized for their mechanical properties through tensile and fracture toughness tests. Results indicate that LDPE/CNT blended with PP/CNT pellets exhibited improved Young’s modulus and fracture toughness, while LDPE/CNT blended with PP/CNT powder showed enhanced stiffness and fracture toughness. The critical stress intensity factor ( KIC) increased with higher proportions of PP in both cases, signifying improved crack resistance. XRD and SEM analyses confirmed enhanced crystallinity and proper bonding between polymers and CNTs. Overall, this study demonstrates the potential of microwave processing in producing nanocomposites with enhanced mechanical properties, offering a promising avenue for engineering applications.

Моделирование упругопластического разрушения компактного образца

The strength of a compact specimen under normal fracture (fracture mode I) is studied within the framework of the Neuber-Novozhilov approach. A model of an ideal elasto-plastic material with limiting relative elongation is chosen as the model of the deformable solid. This class of materials includes low-alloy steels that are used in structures operating at temperatures below the cold brittleness threshold. The crack propagation criterion is formulated using the modified Leonov-Panasyuk-Dugdale model, which uses an additional parameter, i.e., the diameter of the plasticity zone (the width of the prefracture zone). In the case of stress field singularity occurring in the vicinity of the crack tip, a two-parameter (coupled) criterion for quasi-brittle fracture is developed for type I cracks in an elastoplastic material. The coupled fracture criterion includes the deformation criterion attributed to the crack tip and the force criterion attributed to the model crack tip. The lengths of the original and model cracks differ by the length of the prefracture zone. Diagrams of the quasi-brittle fracture of the specimen under plane strain and plane stress conditions are constructed. The constitutive equations of the analytical model are analyzed in terms of the characteristic linear dimension of the material structure. Simple formulas applicable to verification calculations of the critical fracture load and pre-fracture zone length for quasi-brittle and quasi-ductile fractures are obtained. The parameters in the presented model of quasi-brittle fracture are analyzed. It is proposed to select the parameters of the model according to the approximation of the uniaxial tension diagram and the critical stress intensity factor.

Fatigue Analysis of a Cracked Shaft: a Finite Element Modeling Approach

Shafts are typically used in sophisticated mechanisms and machinery which highly depend on shafts for rotatory motion which could lead to the failure. In today’s contemporary, damages caused by cracking on mechanical components and structures have increased, causing crack and structural failure. The failure could be examined by the calculation of stress intensity factor (SIF). Once the shaft reaches the critical SIF (SIFIC), the flaw is initiated and has a potential to propagate upon loading. Typically, the flaw would spread in many patterns and tenders to the formation and initiation of different types of cracks. Thus, the objective of this research work is to analyse fatigue cracked shafts. Prediction of crack growth via SIF calculation. SIF is usually adapted to predict the stress intensity near the crack tip where crack propagation occurs. Thus, SIF is used to study and analyse the cracked surface in relation to crack initiation and propagation. The SIF is calculated through finite element method (FEM) since the FEM is capable simulating complex geometry. The SIF is calculated based on the deformation in FEM calculation. The results show the predicted crack propagation and SIF calculation. It is crucial to study the resistance of cracked shafts towards cyclic loading for maintenance preceding and retirement of the structure.

Effect of filler materials on the tensile properties and fracture toughness of laser beam welded AA2198 joints under different ageing conditions

The influence of different filler materials on the microstructure, tensile mechanical properties, and fracture toughness of laser beam welded AA2198 alloy as well as the effect of different artificial ageing heat treatments were investigated in this contribution. The welded joints were produced when exploited either, Al-Si (AA4047) or Al-Cu (AA2319) filler wires. It was shown that the Al-Si filler wire gave higher hardness values in the fusion zone when compared to the Al-Cu filler wire. The post heat treatment of the welded specimens increased by approximately +100 % the yield stress and by +20 % the ultimate tensile strength with increasing ageing time, in a similar way to the non-welded material. Elongation at fracture decreased in an inverse proportional manner to yield stress. Artificial ageing before welding gave improved elongation at fracture for the over-aged condition only. The quality index concept showed that the artificial ageing before the welding did not succeed in giving a higher quality of the welded joints, for both filler materials investigated. The opposite was shown on the post heat treatment, where the peak-aged condition increased substantially the ‘quality’ of the welded joints with both filler materials. The critical stress intensity factor was increased by +25 % for the under-aged condition for the post-welded condition and both investigated filler wires as a result of the balance between medium values in strength and ductility, respectively.

Nanofracture of graphyne family with geometrical distortions of crack fronts

The static fracture of α-, β-, γ-, and 6,6,12-graphyne under mixed-mode I/II loading in boundary layer models is studied by molecular dynamics and linear elastic fracture mechanics. We find that the crack front undergoes distinct lattice distortions before cracking, which is closely related to the geometric composition of lattices (hexagonal and triangular) in graphynes. Distorted lattices intensify stress concentration around the crack tip during loading. Furthermore, the fracture toughness varies with the graphyne types, among which γ-graphyne shows the highest critical stress intensity factor of 2.0–2.9 MPa·√m, while α-graphyne exhibits the largest critical energy release rate of 8.3–8.9 J/m2. Upon cracking, the crack tends to propagate along the zigzag surface, aligning with the direction of atomic maximum circumferential stress or the local maximum energy release rate. However, the T-stress criterion is limited in determining the cracking direction due to the local anisotropy in graphynes. This study provides plenty insights into the lattice fracture of the graphyne family.

Fracture toughness determination methods of WC-Co cemented carbide material at micro-scale from micro-bending method using nanoindentation

Determining toughness properties is crucial for the development of components made of brittle materials, especially at the microscale. Numerous methods rely on establishing a limit load that triggers the propagation of a pre-cracked specimen. The primary challenge lies in accurately and repeatably determining this limit load value. In this study, we introduce a coupled numerical-experimental approach to determine the stress intensity factor at the microscale using a micro-bending test on pre-notched cemented carbide micro-cantilevers. Specimens are fabricated through micro-electrical-discharge milling, and the initial crack is generated using a focused ion beam process to ensure a repeatable crack shape. Geometries are defined to validate beam theories.Cycling bending tests, employing nanoindentation with three types of loading (fatigue-like, progressive repeated, and ramping sinusoidal loadings), are utilized to ascertain fracture toughness properties of tungsten carbide material at the microscale. Micro-indentation is also conducted conventionally to compare hardness at meso and micro-scales. Analytical methods and finite element analysis are employed to extract the critical stress intensity factor. The cyclic bending test with the proposed ramping sinusoidal loading demonstrates a time shift between the applied force and the displacement, enabling accurate and repeatable detection of the initiation of crack propagation. The primary contributions are associated with the development of a micro-bending test on precracked microcantilevers with ramping sinusoidal loading applied by a nanoindentor device. The miniaturization of specimens and tests, for an equivalent grain size, does not result in a scale effect on toughness properties.

Atomistic fracture in bcc iron revealed by active learning of Gaussian approximation potential

The prediction of atomistic fracture mechanisms in body-centred cubic (bcc) iron is essential for understanding its semi-brittle nature. Existing atomistic simulations of the crack-tip under mode-I loading based on empirical interatomic potentials yield contradicting predictions and artificial mechanisms. To enable fracture prediction with quantum accuracy, we develop a Gaussian approximation potential (GAP) using an active learning strategy by extending a density functional theory (DFT) database of ferromagnetic bcc iron. We apply the active learning algorithm and obtain a Fe GAP model with a converged model uncertainty over a broad range of stress intensity factors (SIFs) and for four crack systems. The learning efficiency of the approach is analysed, and the predicted critical SIFs are compared with Griffith and Rice theories. The simulations reveal that cleavage along the original crack plane is the atomistic fracture mechanism for {100} and {110} crack planes at T = 0 K, thus settling a long-standing issue. Our work also highlights the need for a multiscale approach to predicting fracture and intrinsic ductility, whereby finite temperature, finite loading rate effects and pre-existing defects (e.g., nanovoids, dislocations) should be taken explicitly into account.

Fatigue life assessment of notched laminated composites: Experiments and modelling by Finite Fracture Mechanics

In this paper, the coupled Finite Fracture Mechanics criterion is extended to assess the finite fatigue life of orthotropic notched laminated composites. The approach is validated through a comprehensive experimental program conducted on laminated composites under tension-tension cyclic loading conditions with two distinct lay-ups. For a given loading ratio, fatigue tests on plain and cracked specimens are first performed to provide the model inputs, the critical cyclic stress and stress intensity factor amplitudes. Fatigue tests on samples weakened by circular holes of two different radii are then used for blind predictions. Accurate predictions of the number of cycles to failure are achieved without the need for inverse calibration of material properties or deviation from standard testing procedures. Finally, a parametric study is performed to investigate the hole radius effect. It is worth mentioning that the proposed approach is general and can be applied to any notched geometry.

Influence of high temperatures on modes I and II fracture toughness and energy of nanoclay-reinforced polymer concrete

This paper investigates the influence of exposure to elevated temperatures on the fracture mechanics of polymer concrete (PC). The PC was synthesised using epoxy, silica sand, crushed basalt, and nanoclay. The prepared PC was exposed to temperatures of 24, 40, 60, 80, 100, 120 and 140°C for two hours, and the residual fracture toughness and fracture energy in mode I and mode II were studied. The three-point bending test was conducted on cracked semi-circular bend specimens with a crack angle of 0° (pure mode I) and 41° (pure mode II) to determine the fracture parameters. Subjection to high temperatures significantly increased the fracture toughness and fracture energy of the PC. The maximum fracture toughness and fracture energy were obtained after exposure to temperatures of 120°C and 140°C, respectively. Scanning electron microscopy was used to investigate the fracture surface of the PC. The type of fracture (brittle or ductile) of the PC before and after exposure to the target temperatures was evaluated. The mathematical relationships between modes I and II critical stress intensity factor (KIc and KIIc), as well as modes I and II fracture energy (GIf and GIIf) after exposure to high temperatures, were also determined.

3D numerical analysis of stability and onset of hydraulic fracture in the vertical‐oblique‐horizontal wells under wide range of in situ stresses

AbstractInfluence of the depth and location of perforation, direction and magnitudes of in situ stresses, wellbore angle, and pumping pressure is investigated numerically for the hydraulic fracture. 3D models of rock formation with vertical, inclined or horizontal wells containing semi‐circular crack are analyzed to obtain both KI and the minimum pumping pressure. By computing the magnitude and sign of the T‐stress it is demonstrated that hydraulic fracture path is generally stable except for a very limited situations in which the vertical well is subjected to the lowest in situ stresses. The minimum horizontal in situ stress has the most dominant role in controlling the hydraulic fracture. A direct relationship between KI and T was obtained for different ranges of in situ stresses and some relations were presented for estimating the critical stress intensity factor at the onset of hydraulic fracture and minimum injection pressure in terms of the applied in situ stresses.