Critical Fracture Energy Research Articles

Parametric investigation of bonded composite joints under Mode II using a new methodology based on design of experiments

ABSTRACT In the pursuit of a sustainable future with limited resources and growing environmental concerns, adhesive joining stands out as a pivotal technology for the advancement of lightweight structures. This study aims to investigate the influence of various variables on the critical strain energy release rate in mode II (GIIc) for End-Notched Flexure (ENF) bonded composite joints, employing a new methodology based on Design of Experiments (DoE) approach. Two-dimensional finite element models of the ENF bonded composite joints are developed using commercial software, with all numerical models generated via Python™ scripts linked with AbaqusⓇ. Eleven design parameters related to the specimen geometry and material properties are systematically evaluated to determine the influence of each variable on GIIc. Numerical force–displacement curves are obtained, followed by the application of the Compliance-Based Beam Method (CBBM) to estimate the critical fracture energy in mode II, represented by a numerical envelope. The influence of each parameter is assessed using the main effect (ME) metric. The top five most influential variables affecting GIIc and CBBM are identified as the adhesive’s critical strain energy release rate in mode II (GIIc), effective laminate longitudinal elastic modulus (), adhesive thickness (tA), adherent thickness (h), and pre-crack length (). Furthermore, the study highlights the epistemic uncertainty associated with the geometric variables. Despite the limitations inherent in the computational model, the Plackett-Burman method consistently proves effective in conducting sensitivity analysis of the variables in the ENF test. These findings demonstrate promising prospects for the application of this procedure in the design of composite joint structures.

Finite element modeling of high-speed orthogonal cutting: A contribution to understanding the influence of mesh parameters on saw-toothed chip formation

Modeling of metal cutting using finite element (FE) method has been investigated in many studies. They make it possible to better understand the chip formation. However, the mesh dependence of the numerical solution is still unsolved. The purpose of this paper is the modeling and simulation of saw-toothed chip formation during high-speed orthogonal cutting. Further, the influences of mesh parameters on saw-toothed chip formation are investigated as an innovative highlight of this study. The investigation of high-speed cutting (HSC) is based on FE analysis, where the Johnson-Cook (JC) constitutive model is combined with an energy-based fracture criterion. The mesh parameters considered include element dimension, element orientation, and hourglass treatment. The results show that the peak and valley values of saw-toothed chip obtained through the model mesh10 × 10 are close to the measurements, but the pitch value is predicted with a larger error than those of peak and valley values. Square elements of dimension 10 μm can be also used to avoid the influence of element orientation on cutting forces with an error about 10%. When using square elements, the hourglass treatment causes slightly differences in chip morphology and cutting force. On the other hand, the enhanced is the more efficient method to prevent the hourglass effect for rectangular elements. The model mesh8 × 10 gives an error less than 15% for cutting force. Moreover, the effect of element dimension on cutting force can be reduced by applying the fracture energy criterion controlled through a characteristic length to different mesh dimensions.

Comparative Analysis of Reinforced Asphalt Concrete Overlays: Effects of Thickness and Temperature.

Reflection cracking in asphalt concrete (AC) overlays is a common form of pavement deterioration that occurs when underlying cracks and joints in the pavement structure propagate through an overlay due to thermal and traffic-induced movement, ultimately degrading the pavement's lifespan and performance. This study aims to determine how alterations in overlay thickness and temperature conditions, the incorporation of chopped fibers, and the use of geotextiles influence the overlay's capacity to postpone the occurrence of reflection cracking. To achieve the above objective, a total of 36 prism specimens were prepared and tested using an overlay testing machine (OTM). The variables considered in this study were the thickness of the overlay (40, 50, and 60 mm), temperature (20, 30, and 40 °C), mix type (reference mix and mix modified with 10% chopped fibers by weight of asphalt cement), and the inclusion of geotextile fabric at two positions (one-third of the depth from the base and at the bottom). The research outcomes revealed that a decreased temperature and thicker overlay led to a higher resistance to crack initiation and full propagation, as indicated by the values of critical fracture energy (Gc) and crack progression rate (CPR). Furthermore, the study observed the enhanced crack resistance of overlays in the presence of geotextiles, whether at the bottom or one-third of the depth from the bottom, with superior performance of the former. Despite a slight enhancement in certain properties, the incorporation of chopped fibers in the overlays did not substantially improve the overall performance compared to the reference specimens. Overall, the study provides valuable insights into the variables that influence the ability of AC overlays to mitigate reflection cracking. These findings will aid engineers and designers in making informed decisions regarding overlay design and construction.

Influences of induced heating-healing on fracture properties and life extension of asphalt mixtures: Experimental investigations

In recent years, researchers have concentrated on identifying the effectiveness of induced healing techniques and increasing the healing capacity of asphalt materials. However, the impact of the induced healing method on extending pavement life or the behavior of the pavement in terms of cracking progression has not been evaluated. The main objective of this study is to develop a methodology to evaluate the impact of induced healing on fracture characteristics and life extension of asphalt mixtures. Semi-circular bending (SCB) tests were conducted at both 25 °C and −20 °C. From the SCB test results, fracture-related parameters such as peak load, critical stress intensity factor, strain energy, J-integral, fracture energy, and stiffness were determined. The SCB tests were carried out under cyclic cracking-healing scenarios to assess the effectiveness of the healing process. To quantify the healing efficiency, fracture-related parameters and corresponding healing indices (HI) were measured at each damage cycle. Additionally, service life extensions were calculated based on the analysis of fatigue and thermal cracking resistance. Finally, the HI obtained through other fracture-related parameters were used as a response factor to evaluate the statistical significance of each fracture parameter. The results show that for unaged asphalt mixtures, service life extensions for fatigue and thermal cracking resistance were 3.61 and 3.46 times the initial pavement life, respectively. In contrast, for specimens that experienced 20 years of aging after construction, the corresponding values were 1.50 and 2.23. This suggests that while increasing levels of aging reduce the effectiveness of the induced healing process, the pavement life can still be extended by using the induced healing method. Furthermore, a significant variation was observed in the HI obtained from different fracture-related parameters for asphalt mixtures at different aging levels. This suggests that using the ultimate strength of specimens to determine HI may present conservative results for aged asphalt mixtures since it does not explain the cracking features of the asphalt mixture at intermediate temperatures. The proposed fracture-based method can represent the interactions of cracking and time-dependent behaviors of materials, allowing for the combined effects of the healing process on fatigue and thermal fatigue life extensions to be addressed.

Effects of low cycle impact fatigue on the residual mode II fracture energy of adhesively bonded joints

Cyclic loading exerts a profound influence on the durability of adhesively bonded joints, particularly under cyclic impact loads. Under normal cyclic loading, adhesive joints typically reach their fatigue limit when subjected to approximately 50% of their maximum static strength. However, the endurance limit is considerably lower for cyclic impact loading, sometimes even falling below 5% of the impact strength. This paper investigates the effects of low-energy cyclic impacts on the fracture energy of an end-notched flexure (ENF) joint bonded with an epoxy-based adhesive. The study includes an analysis of the static fracture energy of the ENF joints prior to subjecting them to repeated impact cycles. Additionally, certain joints were subjected to repeated impact cycles until complete crack propagation occurred. To evaluate the residual critical fracture energy of these joints, certain cyclic impact tests were interrupted, and the joints were subsequently subjected to quasi-static loading conditions. The results reveal the remarkable sensitivity of the fracture energy of adhesive joints to the impact energy level, challenging the assumption of infinite life under cyclic impacts often made in conventional fatigue tests. Stress concentration caused by cyclic impact stress waves leads to a higher density of cracks at the specimen edges. The findings are supported by numerical analysis conducted in this study. These results underscore the importance of comprehensive inspections for bonded structures exposed to low-energy cyclic impacts, as impact fatigue can significantly diminish joint strength. The fracture energy decreases as the number of impact cycles increases, indicating a cumulative effect. The findings contribute to a better understanding of the mode II fracture behavior of adhesively bonded joints under repeated impact loads and provide insights for safe design and inspection practices.

Fracture toughness anisotropy of Ti17 disk fabricated by through-transus-processed forging and the role of toughening mechanisms

The fracture toughness anisotropy of the Ti17 disk fabricated by through-transus-processed forging was discussed. For the specimens in different directions, the fracture initiation toughness Ki was calculated through the crack tip opening displacement, and the contribution of the crack tip blunting and dimple formation to the fracture initiation toughness was distinguished. Furthermore, the origin resulting in the fracture toughness anisotropy was analyzed according to the energy criterion for fracture. The results reveal that the specimen directions have a significant influence on the global fracture toughness and the crack propagation path. Meanwhile, the fracture initiation toughness occupies a significant portion of the global fracture toughness, and it reflects the ability of the crack tip plasticity. In addition, a schematic illustration is applied to demonstrate the toughening mechanism. This reveals that the different specimen directions result in the crack deflection or shearing off the ligament, leading to increased fracture toughness compared with the weak specimen direction.

Differential Energy Criterion for Brittle Fracture: Conceptualization and Application to the Analysis of Axial and Lateral Deformation in Uniaxial Compression of Rocks.

This paper discusses modeling the behavior and prediction of fracture of brittle materials. Numerous publications show that progress in this area is characterized by the emergence of a number of new models that meet the requirements of the mining industry, construction and other engineering practices. The authors focus only on one class of models, paying special attention to the compromise between simplicity of solution and versatility of the model. A new version of the model is proposed, taking into account the advantages of previous models. We present a differential energy criterion for brittle fracture substantiated, according to which, fracture occurs at a certain ratio of dissipated and stored (elastic) energy. Fracture is considered as the end of the deformation process with a virtual transformation of the initial material almost without cracks into a real material with cracks. The highest and lowest elastic moduli are analytically determined, respectively, on the ascending and descending branches of the stress-strain curve. A graphical version of the algorithm for determining the brittle fracture point on the post-peak branch of the stress-strain curve is proposed. The modeling results are consistent with the experimental data known from the literature.

ON ONE ENERGY CONDITION FOR THE DEVELOPMENT OF AN ISOLATED CRACK

Based on the energy approach to the brittle fracture process, a new energy criterion of fracture is obtained in the case when an arbitrary normal symmetrical load acts on the surface of an isolated crack.

Effect of NiAl Bond Layer on the Wear Resistance of an Austenitic Stainless Steel Coating Obtained by Arc Spray Process

<div>The present investigation has been conducted to study the tribological and adhesion properties of X10CrNi18-8 austenitic stainless steel (ASTM 301) coatings deposited on aluminum alloys such as AU4G by using the arc-spraying process. These coatings were made with and without a bond-coat layer, which is constituted by NiAl. The structure of the phases that are present in coatings was characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM). The measurements of microhardness and tribological behavior at different loads were also performed on the surface of the coatings. Adherence test was also carried out using four-point bending tests. The SEM showed that the dense microstructures of coatings have a homogeneous lamellar morphology with the presence of porosities and unmelted particles. The main phase of coating corresponds to a solid solution as a face-centered cubic (fcc). The microhardness of coatings is nearly four times that of the two substrates of aluminum alloys. The four-point bending test results showed that the NiAl bond layer increases the critical interfacial fracture energy <i>G</i> <sub>IC</sub>, the force to share the multilayer is more important.</div>

Microstructure- and damage-nucleation-based crystal plasticity finite element modeling for the nucleation of multi-type voids during plastic deformation of Al alloys

During deformation of aluminum (Al) alloys, there are three kinds of voids being formed by distinct mechanisms, i.e., matrix-cracking voids (MCVs), particle-cracking voids (PCVs), and interface-debonding voids (IDVs), due to mesoscale heterogeneous deformation. The three kinds of void nucleation have different effects on the subsequent void growth, void coalescence, and ductile fracture of Al alloys. To determine the complex nucleation behavior of the three kinds of voids under mesoscale heterogeneous deformation, a microstructure- and damage-nucleation-based crystal plasticity finite element (MDNCPFE) model considering different nucleation mechanisms was established. To realize the MDN-CPFE modeling, the deformation and void nucleation of the matrix, particle, and their interface in Al alloys were described by a non-local dislocation density CP constitutive model and a local stored energy density criterion, an elastic constitutive model and a maximum principal stress criterion, and a cohesive zone model and fracture energy criterion, respectively. The developed MDN-CPFE model was validated by the nucleation locations and quantitative variations of the three kinds of voids in an in-situ tensile test. Using the developed model, the nucleation characteristics of the three kinds of voids during the small deformation of Al alloys were analyzed. It is found that PCVs are likely to nucleate within particles that are located at the deformation bands and with greater shape irregularity; IDVs are prone to nucleate at the interfaces around smaller particles in the deformation bands; MCVs tend to nucleate within grains with a higher Schmid factor and aspect ratio. The void area fractions (VAFs) of the three kinds of voids all evolve with an incubation stage and then followed by an exponentially increasing stage during deformation. The duration of the incubation stage for the three kinds of voids, designated by the nucleation strain, presents the following sequence: PCV < IDV < MCV; while, their VAFs and quantities present the opposite sequence. Additionally, the effects of the particle volume fraction and grain size on the nucleation strain, total VAF, and proportion of VAFs of the three kinds of voids were unraveled.

A Cohesive-Zone-Based Contact Mechanics Analysis of Delamination in Homogeneous and Layered Half-Spaces Subjected to Normal and Shear Surface Tractions

AbstractA contact mechanics analysis of interfacial delamination in elastic and elastic-plastic homogeneous and layered half-spaces due to normal and shear surface tractions induced by indentation and sliding was performed using the finite element method. Surface separation at the delamination interface was controlled by a surface-based cohesive zone constitutive law. The instigation of interfacial delamination was determined by the critical separation distance of interface node pairs in mixed-mode loading based on a damage initiation criterion exemplified by a quadratic relation of the interfacial normal and shear tractions. Stiffness degradation was characterized by a linear relation of the interface cohesive strength and a scalar degradation parameter, which depended on the effective separation distances corresponding to the critical effective cohesive strength and the fully degraded stiffness, defined by a mixed-mode loading critical fracture energy criterion. Numerical solutions of the delamination profiles, the subsurface stress field, and the development of plasticity illuminated the effects of indentation depth and sliding distance on interfacial delamination in half-spaces with different elastic-plastic properties, interfacial cohesive strength, and layer thickness. Simulations yielded insight into the layer and substrate material property mismatch on interfacial delamination. A notable contribution of the present study is the establishment of a computational mechanics methodology for developing plasticity-induced cumulative damage models for multilayered structures.

Prediction of ring crack initiation in ceramics and glasses using a stress–energy fracture criterion

AbstractCrack initiation in brittle materials upon spherical indentation is associated with the tensile radial stresses during loading. However, location of crack onset often differs (offset) from the site of maximal stress. In addition, experiments reveal a strong dependency of crack initiation forces on geometrical parameters as well as the surface condition of the sample. In this work, a coupled stress–energy fracture criterion is introduced to describe the initiation of ring cracks in brittle materials, which takes into account the geometry of the contact and the inherent strength and fracture toughness of the material. Several experiments reported in literature are evaluated and compared. The criterion can explain the location offset of the ring crack upon loading, as observed in various ceramics and glasses. It also predicts the ring crack initiation force upon contact loading, provided that surface compressive stresses, introduced during grinding or polishing processes, are taken into account. Furthermore, the stress–energy criterion may be employed to estimate the surface residual stress of ceramic parts, based on simple contact damage experiments.

EFFECT OF THE NUMBER OF THE PASSES ON THE MECHANICAL BEHAVIOUR OF ALUMINUM ALLOY PROCESSED USING EQUAL CHANNEL ANGULAR PRESSING (ECAP)

One of the most important industrial processes used in the production of nanomaterials is the ECAP process. Whereby, nanomaterials are produced in relatively large sizes. In this research, the effect of the number of passes on the mechanical behavior of the engineering material was studied. Where the upsetting test was carried out on samples taken from a metal produced by the ECAP process, then the yield stress, maximum stress, and strain values were determined, as well as the Tresca energy fracture criterion was used, and the results were analyzed and converted into graphic relations. From the results, it was found that these values are highly dependent on the number and type of passes.Keywords: ECAP, Aluminum Alloy, Upsetting Test, Mechanical Properties, Anisotropic.

Differential Energy Criterion of Brittle Fracture as a Criterion for Wood’s Transition to the Plastic Deformation Stage

An experimental study and modeling of the behavior of wood during compression along the fibers was carried out. The nonlinear analytical dependence of the load on the strain was considered. Attention was focused on the post-peak stage of deformation in order to determine the load and displacement at which the transition to the stage of plastic deformation occurs. The work was aimed at substantiating the application of the energy criterion of brittle fracture as a criterion for the transition to the stage of plastic deformation. To achieve this goal, methods of mathematical modeling and analysis of test results were used. As an upshot, a simple and practical procedure was developed to predict the transition point to the above stage of plastic deformation. The simulation results were consistent with laboratory tests of samples and fragments of structures. The practical significance of this criterion lies in its possible use as an additional tool for analyzing the condition of some wooden structures. Energy criteria, including the one mentioned above, belong to fairly universal criteria. Accordingly, the research methodology can be adapted to analyze the behavior of, for example, composites under other types of loads in further studies.

Interface strength investigations of 304 stainless steel/T2 red copper T-type brazed joint based on cohesive zone model

Gas wave refrigerators are a type of refrigeration equipment with broad application prospects. The oscillating tube, its core component, was manufactured by brazing to improve production efficiency. To study the brazing interface strength, a small 304 stainless steel/T2 red copper T-type brazed joint specimen was designed. The tensile process of the brazed joint was simulated using ABAQUS software based on the bilinear cohesive zone model (CZM), and the results were compared with the experimental tensile results. Damage critical stress and critical fracture energy of = 40MPa and = 35 mJ mm−2, respectively, were obtained. A VUMAT subroutine was used to obtain the fatigue life of the specimen, and the errors with the experiment were 1.8% and 5.6%, respectively. It was proved that the CZM can simulate the tensile and fatigue loading processes of T-type brazed joints. The microstructure of the fatigue fracture of the specimen was analyzed using scanning electron microscopy. In addition, the effects of cyclic displacement and base metal thickness on the interface fatigue damage process were simulated and analyzed. The results showed that with an increase in cyclic displacement, the crack initiation life decreased and the crack growth rate increased; the interface damage, the crack length, and the fatigue load increased with the increase in base metal thickness.

Optimization of stone matrix asphalt mixture design based on fracture mechanics approach

Low-temperature cracking is one of the most common pavement distresses that occurred in a short period of service life and is known as premature distress. Stone matrix asphalt (SMA) with gap gradation, which has high strength and rutting performance, should also perform well against low-temperature cracking. So in this research, the criteria of SMA mixture design based on the National Cooperative Highway Research Program (NCHRP) 9–8 were optimized in a way so that SMA has the best performance against low-temperature cracking. Therefore, the optimization process was carried out using the response surface method (RSM) considering the combined effect of compaction energy (Ndesign) and binder content as mixture design factors. The fracture evaluation was done based on stress and energy. So critical stress intensity factor (KIC) and critical fracture energy (Gf) were used as fracture evaluation parameters. After conducting the tests and analyzing the results, it was found that 6.09 % binder with Ndesign = 78 leads to a design with a desirability of 0.869, which passed all the NCHRP 9–8 criteria of the mixture design in line with the maximum fracture performance.

A comparative assessment of different adaptive spatial refinement strategies in phase-field fracture models for brittle fracture

For the smeared approximation of a discrete crack, phase-field fracture simulations of brittle materials require suitable finite element meshes in regions where crack propagation is expected to get an accurate resolution of the phase-field function. The straightforward option is to pre-refine the mesh in regions of the expected crack paths. However, this could lead to very computationally intensive simulations due to the high number of elements. Alternatively, adaptive spatial refinement of the finite element mesh is utilized based on appropriate error indicators to obtain the required accuracy in the areas of crack propagation. Different error indicators can be used: the most common one for phase-field fracture simulations is the threshold-based approach, in which elements are refined depending on the value of the phase-field function. Alternatively, the Kelly error indicator can be used as a criterion for spatial adaptivity. It considers the jumps in the gradients of the phase-field function between the elements. We additionally introduce here an error indicator based on configurational forces, that depend on the Eshelby stress tensor. For mode I loading in linear elastic fracture mechanics, the configurational forces have a close connection to the J-Integral and the critical fracture energy Gc, respectively. Therefore, a suitable norm of the configurational forces is introduced as an error indicator here. These three error indicators are introduced and compared to each other in terms of accuracy and efficiency by means of numerical examples for crack growth in the single edge notched shear test.

Experimental and numerical study of fracturing in degraded and graded crystalline rocks at the laboratory scale

The rock masses are mineral based geomaterials which have been formed by different mineralogical compounds in terms of dimensions and mechanical properties. Geomaterials are often classified as inhomogeneous anisotropic materials due to the orientation of minerals, frequently asymmetric distribution of mechanical properties, porosity, layering, and discontinuities. Differences in deformation properties of mineral crystals under applied stresses is a potential source for crack initiation/propagation in geomaterials. Meanwhile, weathering, alteration, and thermo-chemical agents can change the distribution of mechanical properties by causing unequal effects on different minerals. Redistribution of properties changes the intensity of heterogeneity and anisotropy and ultimately changes the rock fracture mechanism. Therefore, in this study, with the use of transgranular and intergranular enrichment functions and an interaction integral for inhomogeneous materials the failure mechanism of graded and degraded rocks affected by altering factors is simulated. The concept of energy release rate was used to predict the crack initiation angle and the crack trajectory within or between mineral grains. To verify and validate this approach, the results are compared with experimental test results and those reported in the literature. The results show that the crack trajectory significantly depends on the properties of minerals and their boundaries. The smaller the ratio of intergranular to transgranular critical fracture energy is, the more likely the crack to propagate between the grains. Simulation of crack propagation in altered specimens also showed that the crack tends to preferably propagate in weaker minerals. It is also found that using homogenization techniques instead of explicit modeling of minerals may produce inaccurate results. That is because it predicts pure fracture modes at angles in which the mixed tensile-shear modes should be detected.

Direct measurement and verification of cohesive zone model parameters for basalt/PProds using the transverse tensile test and virtual double cantilever beam test

AbstractTo further our understanding of failure in thermoplastic‐based composite rods, the mode I‐governed cohesive zone model parameter of a basalt fiber reinforced polypropylene composite rod is evaluated. The relations between stress and strain, the maximum normal traction and final separation displacement are examined using a transverse tensile test method. The measured traction is verified by three‐dimensional finite element analysis of rod‐shaped double cantilever beam specimens. The numerical results show the close relation between the crack length and cube root of compliance, and yields a representative value of the mode I‐governed critical fracture energy.

Energy Criterion for Fracture of Rocks and Rock-like Materials on the Descending Branch of the Load-Displacement Curve.

This article deals with the problem of predicting the brittle fracture of rocks and similar materials, which can also include frozen sandy soils. Such materials, due to the diversity of their conditions of origin, are characterized by natural heterogeneity at the micro-, meso-, and macro-levels, which makes it difficult to develop sufficiently universal criteria for their strength. Despite a number of known models and criteria of strength and fracture, the search for such criteria remains an urgent problem. In this paper, using the energy approach to the mathematical modeling of mechanical systems, the fracture criterion is justified, which differs from the known criteria that do not require integration to calculate the strain energy We and dissipation energy Wd. The well-known relation for the input energy W=We+Wd is used. The object of the study was the ratio of dW=dWe+dWd. The main research question concerned what the ratio of dWe and dWd would be at the point of brittle failure. The search for an answer to the question led to the justification of a differential energy criterion for the failure of brittle materials on the descending branch of the full stress−strain curve. It was found that the point of predicted fracture is determined by the equality σ=0.5 εEtangential (if there is an inflection point on the ascending branch) or σ=0.5 εEsecant_secant. The main result of the work was ascertaining the differential strength and fracture criteria of brittle materials in the form of inequalities and equations, which were oriented for application in engineering calculations. Examples of application of the developed criteria are given; their consistency with the experimental data known from the literature confirmed.