Cracking Criterion Research Articles

Circumventing cracking in grading 316L stainless steel to Monel400 through compositional modifications in directed energy deposition

In joining Fe-alloys and Cu-containing alloys to access the high strength of steels and corrosion resistance of Cu-alloy, cracking is widely observed due to the significant Cu microsegregation during the solidification process, resulting in an interdendritic Cu-rich liquid film at the end of solidification. By fabricating functionally graded materials (FGMs) that incorporate additional elements like Ni in the transition region between these terminal alloy classes, the hot cracking can be reduced. In the present work, the joining of stainless steel 316L (SS316L) and Monel400 by modifying the Ni concentration in the gradient region was studied. A new hot cracking criterion based on hybrid Scheil-equilibrium approach was developed and validated with monolithic multi-layer samples within the SS316L-Ni-Monel400 three-alloy system and a SS316L to 55/45 wt% SS316L/Ni to Monel400 FGM sample fabricated by direct energy deposition (DED). The new hot cracking criterion, based on the hybrid Scheil-equilibrium approach, is expected to help design FGM paths between other Fe-alloys and Cu-containing alloys as well.

Fatigue cracking prediction of cobblestone interlayer pavement using non-destructive testing and mechanistic-empirical analyses

Several non-destructive testing (NTD) methods have been used to measure surface deflection, which makes to determine the elastic moduli of pavement layers through the back-calculation process and assess the structural capacity of asphalt pavements. In this study was evaluated the back-calculated moduli of the cobblestone interlayer pavements and the load capacity of this type of pavement related to the fatigue cracking criterion based on a mechanistic-empirical analysis. The employed methodology included the performance of on-site trials using non-destructive testing with the Falling Weight Deflectometer (FWD) devices on 84 test points in granular and cobblestone interlayer pavements, determination of deflection basin parameters (DBP), back-calculation layers’ moduli, and estimate of the fatigue cracking performance of the pavements by mechanistic-empirical analyses in MeDiNa software. The pavements with a cobblestone base layer displayed greater deflection measurements on the load application point compared to those measured on pavements with a granular base layer, indicating that conventional pavement displayed more stiffness. Cobblestone interlayer pavement displayed greater amounts of cracked area compared to granular base layer pavements showing lower load capacity based on the fatigue criterion. The DBP-based method by FWD test was able to identify the structural differences between the layers of pavements evaluated and identify the cracking evolution.

New insights into fracture and cracking simulation of quasi-brittle materials based on the NMMD model

The simulation of crack-induced failure is of vital importance for the safety and integrity assessment of solids and structures but still challenging. Being the foremost approach, fracture mechanics is plagued by the logical inconsistency in dealing with crack and non-cracked region, and to make matters worse, it has been contradicted by the ongoing experiments that the fracture energy is not a material constant irrelevant to geometry even for the unsophisticated situations. In this paper, based on the recently proposed nonlocal macro-meso-scale consistent damage (NMMD) model, it is demonstrated that the logical consistency of governing equations either on crack-tip or off crack-tip plays a crucial role in the complete solution of cracking problems. To this end, the central themes of fracture mechanics, including the definition of an idealized crack, the separated equilibrium laws and the cracking criteria attached to crack-tip, are firstly revisited. Then, after a concise description of NMMD model with emphasis on the geometrical transmission form micro- to macro-scale and the physical–mechanical translation from geometry to energy, it is theoretically proved that the geometry-based damage zone reproduces idealized crack as a limit when the nonlocal characteristic length, i.e., the influence radius in NMMD model, tends to zero. As a result, the separated equilibrium laws of fracture mechanics can be covered by NMMD model with a unified set of governing equations that does not distinguish between points at crack surface and at non-cracked region. This advantage permits NMMD model to be well-suited to analyze both crack-induced failure problems with and without pre-existing cracks in the absence of additional cracking criteria. In contrast, owing to its macro-meso-scale consistent feature, a new criterion for kinking angle of crack, the maximum stress intensity factor (SIF) of mode-I, can be derived from NMMD model. Some representative numerical examples are also presented to further confirm the above intrinsic link to fracture mechanics. In particular, the superiority of the NMMD model is demonstrated by capturing not only the non-constant fracture parameters (especially the fracture energy) but also the cracking initiation not from the pre-existing crack-tips, which are revealed by experimental results but contradict fracture mechanics. These investigations imply that the NMMD model could provide a potential avenue to understand when and how cracks nucleate and propagate based on a two-scale perspective.

Understanding the influence of boron in additively manufactured GammaPrint®-700 CoNi-based superalloy

Boron is commonly added to superalloys in small amounts to enhance creep resistance, but can lead to cracking at high concentrations, especially during the additive manufacturing process. Two variants of CoNi-based GammaPrint®-700 superalloy with different B contents (0.08 at% vs 0.16 at%) were printed via laser powder bed fusion (LPBF) with the same printing parameters, with only the high B alloy exhibiting solidification cracking. Atom probe tomography (APT) revealed stronger segregation behaviors in the high B alloy compared to the low B alloy at both the inter-dendritic regions and grain boundaries (GBs). The segregation behavior at inter-dendritic regions was well captured with Scheil simulation and can correlate with the existing cracking susceptibility index (CSI) on cracking tendencies, although high angle GBs are where cracking occurs according to electron backscatter diffraction (EBSD) measurements. Additionally, the extent of GB segregation was compared between the high B and low B alloy. Higher B additions led to significantly more GB B segregation in the high B alloy compared to the low B alloy. For the high B alloy, the cracked region of one GB exhibited higher levels of B compared to the uncracked region of the same GB. However, much higher B contents were also found in two other uncracked GBs in the high B alloy, which demonstrates that higher GB B concentrations are not fully responsible for the cracking. A much larger variance in GB B segregation content was found in the high B alloy compared to the low B alloy. These phenomena were explained with a solidification model with the GB segregation content expressed explicitly by a modified Langmuir-McLean equation. This model linked the GB segregation content with solidification undercooling, which can be used as quantitative cracking criteria for future builds.

Multiple cracking and strain-hardening criteria of Engineered Cementitious Composites (ECC) with river sand

The inclusion of river sand in ECC alters the crack initiation and propagation behavior. As a result, the multiple cracking and pseudo strain-hardening of the river sand ECC (RS-ECC) are different from that of the typical micro-silica sand ECC. This study investigates the strain-hardening criteria for the RS-ECC by considering the matrix as a three-phase material containing pre-existing flaws along the sand/matrix interface with a given size distribution. Micromechanics is used to impart the new mechanisms in the analytic model for the steady-state crack analysis and the formulation of the strain-hardening criteria of ECC incorporating river sand. A probability-based approach is adopted to assess the strain-hardening potential of RS-ECC and validated with experimental results. Results show that the proposed model can predict the tensile properties of RS-ECC, which can be used to guide ingredients selection and components tailoring of RS-ECC to achieve required tensile strain-hardening performance.

Effect of welding current and speed on solidification cracking susceptibility in gas tungsten arc fillet welding of dissimilar aluminum alloys: Coupling a weld simulation and a cracking criterion

In order to study the effect of welding current and speed on the solidification cracking susceptibility of weld, gas tungsten arc welding of a fillet weld with a cold filler wire was simulated. Simulation was conducted for dissimilar welding of Al–Cu–Mg to Al–Mg–Si aluminum alloys with an Al–Mg filler metal at the welding current range of 145–175 A and welding speed of 18–24 cm/min. The outcomes of simulations, namely temperature gradient, velocity of isotherms, and weld chemical composition obtained for various welding currents and speeds, were used as inputs for a solidification cracking model. The results showed that the dimensions of the weld profile obtained from the simulation exhibited good agreement with experimental results. However, a discrepancy of 10–23% was observed between experimental and simulated results in relation to one dimension of the weld profile, i.e. the distance between the fillet weld corners. This discrepancy was addressed to identify the underlying reasons. According to the model proposed in this study for solidification cracking of aluminum alloys, both higher welding current and higher welding speed led to a higher susceptibility to solidification cracking. This result was justified by considering factors such as secondary arm spacing of dendrites, isotherm velocity, backfill time, and chemical composition and viscosity of the weld pool. Weldability tests were employed to validate the model's performance for predicting the solidification cracking susceptibility. Thus, the optimal welding parameters can be chosen in accordance with these results and production demands.

Rotary compression test for determination of critical value of hybrid damage criterion for railway steel EA1T

The article presents and discusses the problem of determining and characterizing the cracking limits of cross-rolled specimens. The limit values were determined in accordance with the hybrid Pater criterion. For the study, the author’s test method was used, which allows the determination of the cracking moment, formed as a result of the Mannesmann effect during the compression of specimens in the channel. In order to determine the values needed to describe the cracking criterion, it was necessary to perform laboratory tests and numerical simulations of the process of compression in the channel of discs made of EA1T steel under hot forming conditions. Experimental tests were carried out for forming processes at 950 °C, 1050 °C and 1150 °C. The tested material had a disc shape with a diameter of 40 mm and a length of 20 mm, during the pressing process the diameter of the disc was reduced to a diameter of 38 mm. The increase in forming temperature caused a significant increase in the forming path until cracking occurred. Numerical tests were carried out in the finite element calculation environment Simufact.Forming 2021. The stress and strain distributions in the specimen axis were analysed during the tests, which were then used to calculate the hybrid cracking criterion limit according to Pater. After calculations according to the Pater criterion and after statistical analysis, the cracking criterion limits were obtained.

Cyclic behaviour modelling of additively manufactured Ti-6Al-4V lattice structures

The present work is concerned with the numerical modelling of the cyclic behaviour of Ti-6Al-4V lattice structures. In the study, diamond structures of titanium alloy produced by the additive laser powder bed fusion (LPBF) method with different degrees of relative density were used. Realistic geometric models of the studied mesostructures were generated using computed microtomography, taking into account the imperfections of the material resulting from the manufacturing process. The numerical calculations also took into account the actual material hardening curve in the elastic-plastic strain range. One of the achievements of this work is the numerical modelling of cyclic loading of realistic mesostructures with their imperfections. The areas of the mesostructures most susceptible to fatigue cracking have been identified and analysed. True hysteresis loops and values of local stress and strain amplitude were determined at the locations of highest stress concentration in cyclically loaded diamond structures. The main achievement of the present work was the modelling of the macroscopic fatigue life of the investigated mesostructures based on the true values of stress and strain at the locations most exposed to fatigue cracking. For this purpose, a stress criterion for fatigue cracking of Ti-6Al-4V lattice structures fabricated by the additive LPBF method was proposed.

Research on mining-induced surface soil cracking mechanism and development depth of downward fracture

In order to reveal the cracking mechanism of surface soil layer caused by coal seam mining, and explore theoretical methods for predicting the development depth of downward fractures during mining. Based on the background of the No. 1–2 upper coal seam mining in Daliuta Coal Mine, combining with fracture mechanics, soil mechanics, physical similarity simulation and numerical calculation methods. The mining-induced cracking mechanism and criterion of surface soil layer were analyzed, the crack development pattern and expansion mechanism were revealed, and the prediction formula of downward crack development depth of surface soil layer was put forward. The research results show that surface cracks mainly occur in the tensile zone, the concentrated tensile stress produced by the subsidence of overburden in the tensile zone can lead to soil cracking. When the surface maximum horizontal tensile deformation exceeds the limit horizontal deformation of soil, the soil layer cracks, and the cracking criterion of the surface soil layer was given accordingly. The soil crack of coal seam mining belongs to the mixed mode crack, and the soil cracks tip starts cracking and expanding along the direction of the maximum principal stress, therefore, the initiation crack angle of soil crack tip was obtained, and the fracture criterion of soil crack was proposed. With the crack propagation and development, the microcosmic crack becomes the macroscopic downward fracture. When the horizontal stress of the soil decreases to the cohesive force of the soil, the downward fracture stops develop, and the calculation formula for the development depth of mining-induced downward fracture was proposed. The development and evolution law of downward fracture was revealed, after the surface cracks, with the advance of the longwall face, the downward crack continues to extend and develop to the deep. Downward fracture develops on the ground surface at the open cut side, the mined-out area and in front of the longwall face, the maximum development depth of downward fracture tends to be stable when the longwall face advances to a certain distance. According to the physical simulation, numerical calculation and theoretical calculation, the development depth of downward fracture in No 1–2 upper coal seam mining is 8.11 m, 8.21 m and 8.14 m respectively. The theoretical prediction formula is reliable, and the results can provide a new method for the research of the development depth of mining-induced surface downward fracture.

Designing Al alloys for laser powder bed fusion via laser surface melting: Microstructure and processability of 7034 and modified 2065

Age-hardenable 2000- and 7000-series aluminium alloys share the ability to achieve outstanding combinations of high specific strength and fracture toughness without including expensive alloying elements such as scandium. Using laser surface melting (LSM), we investigate the suitability of two commercial, high-strength aluminium alloys (ultimate tensile strength ≥ 600 MPa) for laser powder bed fusion (L-PBF). It is revealed that solidification cracks form in both, the third-generation Al-Cu-Li alloy 2065 and the high-Zn containing alloy 7034, with the latter having a lower crack density. Through a combination of microstructural characterisation by SEM, EDS, and EBSD, residual stress analysis and quantitative hot cracking criteria, we deduce that alloy 2065 shows greater potential for L-PBF application despite its slightly higher crack density after LSM. Through laser surface alloying, the composition of alloy 2065 was systematically varied in terms of titanium and copper content to improve its cracking resistance. It is found that the formation of solidification cracks is suppressed by the addition of 2 – 4 wt% Ti, whereas the introduction of copper has little effect. Our study suggests that Ti-modified 2065 is an attractive alloy for L-PBF. It could potentially join the existing high-strength aluminium feedstock materials available for L-PBF.

Computational multiphase micro‐periporomechanics for dynamic shear banding and fracturing of unsaturated porous media

AbstractDynamic shearing banding and fracturing in unsaturated porous media are significant problems in engineering and science. This article proposes a multiphase micro‐periporomechanics (PPM) paradigm for modeling dynamic shear banding and fracturing in unsaturated porous media. Periporomechanics (PPM) is a nonlocal reformulation of classical poromechanics to model continuous and discontinuous deformation/fracture and fluid flow in porous media through a single framework. In PPM, a multiphase porous material is postulated as a collection of a finite number of mixed material points. The length scale in PPM that dictates the nonlocal interaction between material points is a mathematical object that lacks a direct physical meaning. As a novelty, in the coupled PPM, a microstructure‐based material length scale is incorporated by considering micro‐rotations of the solid skeleton following the Cosserat continuum theory for solids. As a new contribution, we reformulate the second‐order work for detecting material instability and the energy‐based crack criterion and J‐integral for modeling fracturing in the PPM paradigm. The stabilized Cosserat PPM correspondence principle that mitigates the multiphase zero‐energy mode instability is augmented to include unsaturated fluid flow. We have numerically implemented the novel PPM paradigm through a dual‐way fractional‐step algorithm in time and a hybrid Lagrangian–Eulerian meshfree method in space. Numerical examples are presented to demonstrate the robustness and efficacy of the proposed PPM paradigm for modeling shear banding and fracturing in unsaturated porous media.

Analysis of Implementation Plans for the ACR -PCR System on Flexible Pavement Runways at Utilization Cooperation Airport

ICAO determined that the ACR–PCR system will take effect in July 2020 and be effective in November 2024. It is very important for airports in Indonesia to make adjustments to optimize the use of pavement assets. The research aims to calculate ACR-PCR, compare it with ACN-PCN, evaluating the airside pavement structure of airport through the application of the ACR-PCR system. Case study analysis of calculations with ICAO–ACR1.32 and FAARFIELD2.0. ACN/PCN and ACR/PCR ratios are classified against pavement strength limitation criteria. Evaluation based on the criteria for permanent deformation of the subgrade layer andfatigue cracking of the asphalt layer. Tjilik Riwut airport runway PCR value 542FBXT, Radin Inten II 850FCXT, Fatmawati Soekarno 712FCXT and H. AS. Hanandjoeddin 643FCXT. Comparison of the ACR/PCR and ACN/PCNratiosshows an increase in pavement capacity of 1.4746. Based on the criteria for fatigue cracking of the asphalt layer and permanent deformation of the PCR subgrade layer at Tjilik Riwut airport 668 and 575 FBXT, Radin Inten II 1027 and629FCXT,Fatmawati Soekarno 862 and 629 FCXT, H. AS. Hanandjoeddin 675 and 560 FCXT. The structural pavement capacity of PT Angkasa Pura Indonesia airport has the opportunity to be increased in terms of flight frequency.

High-fidelity simulations of low-velocity impact induced matrix cracking and dynamic delamination progression in CFRP beams

A high-fidelity finite element model is constructed to simulate the low-velocity line-impact experiments conducted by Bozkurt and Coker on [05/903]s CFRP beams. The simulations utilize a user-implemented three-dimensional continuum damage model with the LaRC05 criterion for matrix cracking, and a built-in cohesive zone model for delamination in ABAQUS/Explicit. The significant influence of boundary supports on the global impact response leads to proposing a heuristic boundary conditions approach using spring elements that replicate the experiment boundaries. Results then demonstrated an excellent agreement with the experiments in terms of the global impact response, the strain field, and damage pattern and sequence. Simulations reveal intersonic delamination with crack tip speeds around ∼5000 m/s, while the experimental crack speeds were measured as sub-Rayleigh speeds reaching ∼1000 m/s. When a crack tip definition based on the crack tip opening is introduced in the simulations, crack tip speeds in the range of 490–1500 m/s are measured which are within the range of experimental speeds, suggesting that the sliding mode might be physically hidden in the experiments. The potential use of delamination crack tip speeds as a benchmark for refining numerical simulations is demonstrated by increasing the effective interface toughness leading to a decrease in crack tip speeds with no noticeable effect on the global responses.

The Two-Parameter Fracture Criterion Taking into Account Two-Dimensional Deformation Constraints at the Front of a Mixed-Type Crack

In this article, a new fracture criterion for a mixed-type crack (type I + type II) is proposed. It is based on the assumption that the maximum tangential stresses in the prefracture region are equal to the local strength of the material. In this case, the size of the prefracture area and the local strength are determined taking into account nonsingular Тхx and Тzz stresses included in the expansion of the Williams stress function. The use of Тхx and Тzz stresses in the calculations allows one to describe the two-dimensional local constraint of the deformation along the crack front in three-dimensional bodies. In addition to KI and KII, the expression for the effective stress intensity factor (SIF) includes the ratios of the Тхx and Тzz stresses to the yield strength. This makes it possible to take into account the constraint of deformations in the transverse and longitudinal directions of the crack front, respectively. An example of the implementation of the developed criterion in relation to the determination of the fracture load of a tensile-stressed plate with a through inclined crack is given. Dependences of the Тxx and Тzz stresses on the plate thickness are presented for various crack slopes and plate thicknesses. It is shown that an increase in the plate thickness and a decrease in the crack slope lead to a decrease in the fracture load.

Applying Modified SKK Hot Cracking Criterion to Fusion Welding of Al Alloys

Applying Modified SKK Hot Cracking Criterion to Fusion Welding of Al Alloys

A node-splitting lattice spring model coupled with a J-integral formulation as a fracture criterion

A global energy minimization criterion based on Griffith’s theory is introduced for the node-splitting lattice spring model. The fracture criterion is computed by both direct numerical simulations of energy release rate G and through a J-integral formulation for comparison and validation. For mode I fractures, the standard implementation of J-integral formulation yields very good estimations of the energy release rate, but for mixed mode fracture the estimations deviates from the direct calculated energy release rate. The reasons for this discrepancy are elucidated and an approach to best approximate the J value is given. This method is compared with the more standard maximum tip stress threshold crack criterion, and shows a much better prediction of the energy release rate and is more robust under grid refinement.

The Two-Parameter Fracture Criterion Taking into Account Two-Dimensional Deformation Constraints at the Front of a Mixed-Type Crack

In this article, a new fracture criterion for a mixed-type crack (type I + type II) is proposed. It is based on the assumption that the maximum tangential stresses in the prefracture region are equal to the local strength of the material. In this case, the size of the prefracture area and the local strength are determined taking into account nonsingular Тхx and Тzz stresses included in the expansion of the Williams stress function. The use of Тхx and Тzz stresses in the calculations allows one to describe the two-dimensional local constraint of the deformation along the crack front in three-dimensional bodies. In addition to KI and KII, the expression for the effective stress intensity factor (SIF) includes the ratios of the Тхx and Тzz stresses to the yield strength. This makes it possible to take into account the constraint of deformations in the transverse and longitudinal directions of the crack front, respectively. An example of the implementation of the developed criterion in relation to the determination of the fracture load of a tensile-stressed plate with a through inclined crack is given. Dependences of the Тxx and Тzz stresses on the plate thickness are presented for various crack slopes and plate thicknesses. It is shown that an increase in the plate thickness and a decrease in the crack slope lead to a decrease in the fracture load.

Bond-based nonlocal models by nonlocal operator method in symmetric support domain

The present study focuses on the applications of energy decomposition in diverse nonlocal models, such as elasticity, thin plates, and gradient elasticity, with the aim of establishing bond-based nonlocal models in which the bond force is solely dependent on the deformation of a single bond. Through the adoption of an appropriate bond force form and the application of energy equivalence between local and nonlocal models, several kinds of highly succinct bond-based models are obtained. The present study involves a reexamination of nonlocal operator methods, with a particular focus on the simplified version within a symmetric support domain. A three-point bent-bond model has been proposed to characterize the curvature and bending moment. A crack criterion for normal strain of the bond based on Griffith theories is proposed. This approach is analogous to the phase field model and allows for individual application to each bond, resulting in strain localization. By implementing this rule, the path of the crack can be predicted in an automated manner through the act of cutting the bond, yielding outcomes that are akin to those obtained via the phase field method. Simultaneously, a crack rule for critical shear strains in shear fractures is presented. Moreover, an incremental version of the plasticity model associated with bond force has been formulated. The nonlocal bond-based models are further validated through several numerical examples.

Prediction of Crack Width in RC Piles Exposed to Local Corrosion in Chloride Environment.

A novel prediction model for crack development of reinforced concrete (RC) piles with localized chloride corrosion in the marine environment is proposed. A discrete method is used to solve the corrosion pit radius model and a crack extension model is developed to investigate the initiation and extension of cracks. The maximum corrosion degree of the reinforced concrete pile is predicted according to the limit crack criterion, and finally, a sensitivity analysis is carried out on the important parameters of crack extension. The results show that the radius of the corrosion pit, the depth corrosion pit, and the cross-sectional area loss of reinforcement gradually increase as the corrosion level increases. The loss of the local reinforcement section at crack initiation increases with the increase in the ratio of concrete cover to initial diameter and increases with the increase in the pitting factor. The required pit depth for reinforcement cracking increases with the increase in the ratio of concrete cover thickness to diameter. The loss of the cross-sectional area of reinforcement and the radius of the corrosion pit increase with the increase in the initial diameter of reinforcement. Increasing the pitting factor can reduce the pit depth and make the crack width develop faster before reaching the limit crack width. Increasing the concrete cover thickness can provide an improvement in the propagation of cracks. A comparative analysis shows that the localized corrosion pattern is more in conformity with marine engineering practice.

Comparison of Various Intrinsic Defect Criteria to Plot Kitagawa-Takahashi Diagrams in Additively Manufactured AlSi10Mg.

Selective laser melting is a form of additive manufacturing in which a high-power density laser is used to melt and fuse metallic powders to form the final specimen. By performing fatigue and tensile tests under various loading conditions, the study sought to establish the impact of internal defects on the specimens' fatigue life. Scanning electron microscopy and finite element simulation were conducted to determine the defect characteristics and the stress intensity factor of the specimens. Four different methods were used to determine the intrinsic defect length of the specimen, using data such as grain size, yield strength, and hardness value, among others. Kitagawa-Takahashi and El-Haddad diagrams were developed using the results. A correction factor hypothesis was established based on the deviation of measured data. Using Paris law, fatigue life was determined and compared to the experimental results later. The study aims to select one or more approaches that resemble experimental values and comprehend how internal defects and loading situations affect fatigue life. This study's findings shed light on how internal defects affect the fatigue life of selective laser-melted AlSi10Mg specimens and can aid in improving the fatigue life prediction method of additively manufactured components, provided an appropriate intrinsic crack criterion is selected.