Cracking Criterion Research Articles

Quasi-static crack propagation with a Griffith criterion using a variational discrete element method

A variational discrete element method is applied to simulate quasi-static crack propagation. Cracks are considered to propagate between the mesh cells through the mesh facets. The elastic behaviour is parametrized by the continuous mechanical parameters (Young modulus and Poisson ratio). A discrete energetic cracking criterion coupled to a discrete kinking criterion guide the cracking process. Two-dimensional numerical examples are presented to illustrate the robustness and versatility of the method.

Development of higher-order displacement discontinuity method to simulate fatigue crack growth in brittle materials

The 2D displacement discontinuity method (2D. DDM) is an indirect boundary element technique in which the stresses and displacements are expressed through normal and shear displacement discontinuities. The governing equations of fatigue crack growth are mostly power equations that depend on the stress intensity factor range. Accurate calculation of displacement discontinuity has importance in fatigue analysis of DDM. Therefore, in this study, DDM is extended using cubic variations of displacement discontinuity for ordinary and crack tip elements. This method also uses an appropriate algorithm based on the linear elastic fracture mechanics (LEFM) principle to analyze crack growth under cyclic fatigue loading. This process is accomplished by assuming the homogeneity of brittle material and the small plastic zone of the crack tip compared to the crack dimension. The condition of applying constant and stationary variable amplitude loading was provided. The algorithm is designed based on an iterative process, and the new incremental elements gradually are added to the crack tip until the failure criteria are reached; The size of these elements at each step of growth depends on the crack growth rate in the previous step. Therefore, the fatigue modeling of the structures with multiple cracks and different growth rates is enabled. Virtual crack criteria were employed to improve the accuracy and speed of analysis, which involves crack tips with a slower growth rate. Moreover, the direction of crack propagation is evaluated using the maximum circumferential stress criterion. Examples of simple and multi-fractured structures under constant and variable amplitude load are considered. Comparison of results with literature data shows excellent agreement with high accuracy.

Rheological Analysis of Performance Grade Rutting and Fatigue Cracking Criteria in Asphalt Binders

Rheological Analysis of Performance Grade Rutting and Fatigue Cracking Criteria in Asphalt Binders

Quantitative Assessments of Crack Sealing Benefits by 3D Laser Technology

Crack sealing is one of the most commonly used methods to preserve asphalt pavements. However, quantification of crack sealing benefits (or the long-term delaying effects of crack sealing on crack propagation) remains unavailable because field crack lengths could not be measured accurately and efficiently. In this study, 3D laser technology is proposed to measure and compare the growth of crack lengths between sealed and non-sealed pavement sections and, for the first time, to accurately and efficiently quantify the crack sealing benefits. To validate the proposed method and find adequate treatment timing (or conditions), nine field sites in Georgia, U.S., with different pavement pre-treatment conditions and roadway environmental factors were monitored over 3 years from December 2016 to September 2019. The study results showed that crack sealing can retard crack growth by 40%–128%, and such delaying effects are more significant under better pavement pre-treatment conditions. The findings suggest that transportation agencies can prolong the service life of pavements by applying crack sealing before the pavement condition becomes poor. In addition, this work has been proved to be very valuable for transportation agencies to determine the best timing and treatment criteria for crack sealing.

A comparative analysis of hot and cold flashless forging of a stepped shaft using vertically-parted dies

Flashless forging is classified as a precise metal forming technology. The main advantages of this technology are the reduction of the flash allowance and the shortening of the manufacturing time by eliminating the flash trimming operation. The article presents the process of one-step forging of a stepped shaft made of aluminum with the use of split dies. The process was carried out in cold and hot metal-forming conditions. The forging process was analyzed numerically using the Simufact Forming 15.0 software. The geometrical parameters of the obtained product were analyzed, and the distribution of effective strain, temperature, and the standardized cracking criterion was determined. The process force parameters were also determined. Numerical tests were verified in real conditions with the use of a specially designed device for forging in vertical split dies. Comparison of hot and cold forging in vertical split dies is presented. The comparative analysis results have demonstrated that the hot forging process has more advantages than the cold forging process. The hot forging process ensures higher accuracy of forged parts.

A new meshless Fragile Points Method (FPM) with minimum unknowns at each point, for flexoelectric analysis under two theories with crack propagation, II: Validation and discussion

In the first part of this two-paper series, a new Fragile Points Method (FPM), in both primal and mixed formulations, is presented for analyzing flexoelectric effects in 2D dielectric materials. In the present paper, a number of numerical results are provided as validations, including linear and quadratic patch tests, flexoelectric effects in continuous domains, and analyses of stationary cracks in dielectric materials. A discussion of the influence of the electroelastic stress is also given, showing that Maxwell stress could be significant and thus the full flexoelectric theory is recommended to be employed for nano-scale structures. The present primal as well as mixed FPMs also show their suitability and effectiveness in simulating crack initiation and propagation with flexoelectric effect. Flexoelectricity, coupled with piezoelectric effect, can help, hinder, or deflect the crack propagation paths and should not be neglected in nano-scale crack analysis. In FPM, no remeshing or trial function enhancement are required in modeling crack propagation. A new Bonding-Energy-Rate(BER)-based crack criterion as well as classic stress-based criterion are used for crack development simulations. Other complex problems such as dynamic crack developments, fracture, fragmentation and 3D flexoelectric analyses will be given in our future studies.

A mechanistic framework for tensile fatigue resistance of asphalt mixtures

Fatigue life is one of the most critical factors for asphalt pavement design, which is directly affected by the fracture properties of asphalt mixtures. This study aimed to present a mechanistic framework to determine the Paris’ law parameters A′ and n′ of asphalt mixtures and fatigue life of asphalt pavements. The dynamic modulus test and indirect tensile (IDT) test results were obtained from Texas Data Storage System (DSS) to evaluate the linear viscoelastic properties and fracture properties. Modified Griffith crack criterion in tension was used to determine the damage density rate and pseudo J-integral of macrocracks appeared in the post-peak phase of the IDT test, and the damage density with time was shown as a sigmoidal shape from microcracking initiation. The Paris’ law parameters were then computed using the regression analysis in the macrocracking stage. It was shown that the fracture resistance of asphalt mixtures could be characterized using n′, and a smaller value of n′ indicates a better fracture resistance. The mode-I fatigue life equation for reflection cracking in asphalt pavements was also proposed based on the J-integral from the finite element model and Paris’ law parameters, which shows that the empirical fatigue life transfer function could also be determined from actual material properties and pavement structural boundary conditions.

Development of the MES criterion for brittle fracture prediction in V‐shaped notches under mixed mode I/II loading conditions

AbstractIn this paper, a new brittle fracture criterion was developed to predict the fracture in sharp V‐shaped notches. This criterion, by defining a quantity called “V‐shaped notch effective stress,” takes into account the effect of the shear stress in addition to the tangential stress. The initial crack criterion, which lays the foundation for developing this criterion, has yielded remarkable results for a broad spectrum of brittle materials in the entire range of mixed‐mode I/II loading conditions. This development helps to employ a novel criterion for V‐shaped notches with the capability of being used in the entire range of mixed‐mode I/II loading conditions. The outcomes of the two other valid criteria and multiple experimental results were compared with the developed criterion results to validate it. The developed criterion's predicted results revealed a strong correlation with experimental results, particularly in conditions where mode II loading was predominant.

Predictive Computational Model for Damage Behavior of Metal-Matrix Composites Emphasizing the Effect of Particle Size and Volume Fraction.

In this paper, an integrated numerical model is proposed to investigate the effects of particulate size and volume fraction on the deformation, damage, and failure behaviors of particulate-reinforced metal matrix composites (PRMMCs). In the framework of a random microstructure-based finite element modelling, the plastic deformation and ductile cracking of the matrix are, respectively, modelled using Johnson–Cook constitutive relation and Johnson–Cook ductile fracture model. The matrix-particle interface decohesion is simulated by employing the surface-based-cohesive zone method, while the particulate fracture is manipulated by the elastic–brittle cracking model, in which the damage evolution criterion depends on the fracture energy cracking criterion. A 2D nonlinear finite element model was developed using ABAQUS/Explicit commercial program for modelling and analyzing damage mechanisms of silicon carbide reinforced aluminum matrix composites. The predicted results have shown a good agreement with the experimental data in the forms of true stress–strain curves and failure shape. Unlike the existing models, the influence of the volume fraction and size of SiC particles on the deformation, damage mechanism, failure consequences, and stress–strain curve of A359/SiC particulate composites is investigated accounting for the different possible modes of failure simultaneously.

A field-enriched finite element method for simulating the failure process of rocks with different defects

A field-enriched finite element method is proposed in this paper to simulate the failure process of rocks. According to the different types of defects, the proposed method can select the appropriate failure criteria for voids and cracks. Field variables are used to characterize the crack location and to realize the influence of cracks on the physical field of the numerical model. The main features and the capability of the field-enriched finite element method to efficiently simulate the failure process of rocks with different defects are illustrated with some numerical examples. The results show that the field-enriched finite element method proposed in this paper can obtain the crack propagation path which is consistent with other numerical methods and experimental observations. Moreover, the numerical method proposed in this paper has the advantages of simple implementation process and higher computational efficiency and accuracy in some cases. Therefore, it is a promising numerical simulation method.

Analysis of equivalent temperature to design of asphalt pavements in Poland using the AASHTO 2004 method

Abstract: The paper presents the analysis of the equivalent temperature on the basis of the fatigue cracking criterion of asphalt layers according to the AASHTO 2004 method and the structural deformation of subgrade criterion according to the Asphalt Institute procedure. The calculations were made with application of the KR5 pavement structure and temperature data obtained from 50 meteorological stations and from the period of 30 years from 1989 to 2019, provided by the Institute of Meteorology and Water Management. The influence of variable traffic with heavy vehicle traffic was taken into consideration, both during the day and throughout the year. It was presented how the values of the equivalent temperature change in the territory of Poland depending on the location of the meteorological station. The computational analysis showed the variability of the equivalent temperature on the territory of Poland in the range from 14.68°C (Suwalki) to 16.99°C (Tarnow).The weighted mean value of the equivalent temperature for the entire year is 16.01°C and it is higher than the value adopted in the catalogue of typical flexible and semi-rigid structures that is equal to 13,00°C. The change in the equivalent temperature value on the designed thickness of asphalt layers of the pavement structure has been also assessed in the paper. Keywords: Pavement design; Equivalent temperature; Fatigue life; AASHTO 2004 method

An improved ring test to assess cracking resistance of concrete under restrained shrinkage

Self-restraint caused by differential shrinkage along the radius of a concrete ring has great driving effect on the restrained cracking in the traditional ring test. In order to estimate cracking potential of concrete under restrained shrinkage, i.e. steel ring restraint effect, an improved circular/elliptical ring test was proposed by pre-setting a 6 mm long real crack at the inner circumference of the concrete specimen. Meanwhile, a numerical study based on fracture theory was conducted to investigate the cracking mechanism of the improved ring test. By introducing the fictitious crack model, the crack initiation age and propagation process in the ring specimen were simulated using the initial fracture toughness-based cracking criterion. The driving forces of the shrinkage cracking, provided by self-restraint and steel ring restraint, were analyzed and the influence of the pre-set crack length on the cracking age was discussed. The results indicated that, different from the traditional ring test, the shrinkage crack firstly initiated from the pre-set crack and then unstably propagated toward the outer circumference of the concrete in the improved method. In the crack propagation process, the self-restraint provided cracking insistence rather than driving force on the shrinkage cracking due to the bending effect along the radial direction caused by non-uniform moisture distribution in concrete. Therefore, the driving force of the shrinkage cracking was totally provided by the steel ring restraint and would overcome the cracking resistances from concrete material and non-uniform shrinkage. Furthermore, the advantage of the elliptical geometry in increasing the restraining level was still available for the improved ring test with a pre-set crack, which could make the shrinkage cracking occur in advance and enhance the steel ring restraint.

Performance of field produced rejuvenated 30% RAP surface mix in Northwest Iowa

In this research, as part of a broad investigation, it was determined that 3.6% epoxidized methyl soyate (EMS) by weight of PG 58-34H binder (0.125% by total mix weight) was needed to achieve a PG 52-40H binder due to there being 30% RAP in the mix design (29.80% in the total binder content). Both lab and field produced mix verification showed that 0.125% EMS met the criteria for moisture susceptibility/rutting and low temperature cracking according to Iowa DOT specifications. For comparison purposes, there was a Control mix (PG 58-34H binder and 18% RAP) with no rejuvenator, and a 30% RAP mix design made using a commercial tall oil derivative (CTOD) rejuvenator from the contractor of which both met Iowa DOT criteria for low temperature cracking, but that the Control group did not have adequate rutting performance for a binder rated as PG 58-34H. Initial comparisons between lab low temperature mix performance from field produced and lab compacted specimens to field transverse cracking measurements (1 year after construction) lined up fairly well with trends from previous works for all three groups.

The role of liquid feeding in nugget-edge cracking in resistance spot welding of dissimilar magnesium alloys

In fusion welding, cast magnesium alloys typically present higher sensitivity to liquation cracking than wrought alloys. In this study, a fluid-mechanics-based analytical model was established to investigate an unusual phenomenon: a lack of cracking in cast magnesium alloy while cracking took place in wrought magnesium alloy. This was observed in resistance spot welding, in which the pressure within the molten nugget allows the liquid to feed through the interface between the fusion zone and the partial melting zone, an aspect which is not generally considered in the typical criteria for liquation cracking. The analytical model shows that the liquid is easy to feed into the inter-grain zone of a cast coarse-grained metal but difficult to feed into wrought metal. The liquid feeding effect changes the composition of the inter-grain region, causing the semi-solid grains to bond to each other tightly in the cast magnesium alloy. Electro-probe microanalysis illustrates the mass transfer pattern of liquid feeding at the interface between the fusion zone and the partial melting zone. Magnesium alloys AZ31, AZ91, and ZK61 were selected to carry out resistance spot welding tests of which results match the theory raised in this work well.

Experimental investigation on infrared radiation features of fracturing process in jointed rock under concentrated load

In case of earthquakes and crustal movement, the concentration of impounding load over a large region of crust can cause disturbances to the stratum. In order to quantitatively investigate crack initiation, propagation and coalescence processes of jointed stratum based on thermal variations caused by concentrated load, a series of indentation tests were performed on jointed granite specimens, failure process was respectively recorded by synchronized digital image correlation system and infrared camera. Then, strain and infrared radiation temperature of mixed shear-tensile and tensile conical crack were analyzed. In the initiation process, experimental results indicate that the abnormities in the temperature concentration factors are caused by the frictional-thermal effect for mixed mode crack and the thermoelastic effect for tensile mode crack. Subsequently, in the propagation process, these two cracking types followed newly proposed criteria, namely, the maximum temperature gradient criterion for mixed mode crack and the minimum temperature gradient criterion for tensile mode crack. In addition, the intensity of temperature concentrations in crack initiation stage and coalescence stage are more pronounced than that of crack propagation stage. The new findings from the infrared radiation temperature distributions provide some fundamental references for geophysical prospecting in jointed rock mass.

Non-propogation crack criteria and fracture criteria in the case of mixed-mode fracture, taking into account the deterioration

The paper develops in the case of mixed-mode fracture: criteria of nonpropagation crack and fracture criteria, for mechanical structures, taking into account the deterioration, namely general relations for the superposition of loadings corresponding to the three fracture modes. It refers to the concepts of stress intensity factor, crack tip opening displacement and J-integral; new fracture criteria taking into account the deterioration, the rate of loading and the scattering of the material characteristics were established. The relations obtained have been compared and verified against experimental data and empirical relations reported in literature. The numerical example allows one to comprehend the practical use of the established relations.

An axisymmetric ordinary state-based peridynamic model for thermal cracking of linear elastic solids

This paper proposes an axisymmetric ordinary state-based peridynamic model considering the thermal expansion effect for temperature-induced cracking of linear elastic solids. Both the force state and bond failure criterion of the model are built in axisymmetric domain. The direct calculation for peridynamic bond energy density of the axisymmetric model considering thermal terms is given. The adaptive dynamic relaxation method is adopted for the quasi-static peridynamic simulations. Validity and reliability of the proposed axisymmetric model are illustrated by numerical examples of cold-induced fracture in a pipe with an inner crack. It is shown that the displacement predicted by the proposed peridynamic model is in good agreement with the corresponding finite element method. The critical bond energy density criterion for thermal cracking is verified via comparisons with the critical fracture temperature loads computed from the virtual crack closure technique and released energy based on Griffith’s theory. The sensitivity of the present model on the peridynamic discretization is investigated and discussed in both the continuous deformation and cracking cases. The performance of the peridynamic model is further demonstrated for cold-induced fracture of double-layered pipes with inner cracks, and the cracking behaviors influenced by the interfacial toughness and number of inner cracks are captured, respectively. The present model is capable of solving axisymmetric thermal cracking problems of linear elastic solids effectively, and it can be applied in more advanced axisymmetric structures which involve more complicated cracking issues.

Study on Formation Mechanism of Zonal Disintegration of Surrounding Rock in Deep Tunnel

With the construction of underground rock engineering, the surrounding rock in deep tunnels appears zonal disintegration of fracture and intact zones alternate distribution, which is a special engineering geological phenomenon. This study establishes a partitioned fracture model under the coupling of high in-situ stress and osmotic pressure, and identify the key influencing factors of the fracture model. Furthermore, a stress intensity factor (SIF) of initial cracks on surrounding rock elastoplastic boundary is derived using the transformation of complex functions. Considering the high seepage pressure of the surrounding rocks, a zonal fracture initiation criterion is established combined with the analysis of redistributed stress fields. Finally, the obtained criterion is embedded into an extended finite element method (XFEM) platform for numerical simulation. Taking the maximum circumferential tensile stress as a cracking criterion, the propagation trajectory of rock cracks is traced by contour methods. Calculation results have realized the modelling of a whole process of crack initiation, propagation, and formation. And the established criterion has be verified.

The study of central cracking mechanism and criterion in cross wedge rolling

Cross wedge rolling (CWR) is an innovative metal forming process to manufacture axisymmetric stepped shafts used in the transport industry. Central cracking, also called the Mannesmann Effect, consistently occurs in the central region of the CWR workpiece. This results in reduced product quality and increased costs due to rejected and failed parts. However, the understanding of central cracking mechanism and criterion is limited due to the complex stress states in CWR and the experimental limitations. A large number of CWR tests and different die geometries are required in the identification of the potential mechanistic factors such as the axial tensile stress, secondary tensile stress, shear stress and cyclic loading. Also, there is as yet no efficient method of determining the material constants associated with the central cracking fracture criteria. These problems are addressed in the present study. A physical model was built to reproduce the industrial CWR process. A newly designed model material (plasticine/flour composite) was used to mimic the material flows and internal fracture behaviours found in commercial CWR workpieces. This allowed a variety of die shapes to be rapidly and cost-effectively 3D printed, thereby enabling specific stress states to be achieved within the workpiece. Via experimental observations and the corresponding finite element modelling under different die geometries, the maximum shear stress was identified as the dominant factor for central cracking. The fracture criterion involving the maximum shear stress was quantitatively verified to be accurate and robust in predicting central cracking moments and locations. A novel approach using simplified die geometries to determine the associated material constants was proposed and validated. The high accuracy and cost/time efficiency of this new approach will be a significant benefit to fundamental research and also in industrial applications.

A generalised hot cracking criterion for nickel-based superalloys additively manufactured by electron beam melting

Abstract The influences of microstructure and solidification parameters on the hot cracking behaviour of an additively manufactured Ni-based superalloy via selective electron beam melting (SEBM) have been investigated. Severe intergranular hot cracking is found to occur at grain boundaries (GBs) in the SEBM-built superalloy. A generalised cracking criterion that considers various process parameters along with the GB inclination is developed on the basis of a prevailing hot cracking criterion for columnar-grained microstructure. A parametric evaluation of influencing factors is quantitatively conducted to predict the optimal conditions that could prevent hot cracking while maintaining the desirable fine microstructure. With the aid of numerical simulations, it is determined that while micro-segregation occurs at all types of GBs, its occurrence at the divergent ones tend to promote cracking. Using the results of this work, hot cracking in additively manufactured Ni-based superalloy single crystals can be potentially mitigated.