Fracture Mechanics Model Research Articles

A Stress-State-Dependent Sliding Wear Model for Micro-Scale Contacts

Abstract Wear is a complex phenomenon taking place as two bodies in relative motion are brought into contact with each other. There are many different types of wear, for example, sliding, fretting, surface fatigue, and combinations thereof. Wear occurs over a wide range of scales, and it largely depends on the mechanical properties of the material. For instance, at the micro-scale, sliding wear is the result of material detachment that occurs due to fracture. An accurate numerical simulation of sliding wear requires a robust and efficient solver, based on a realistic fracture mechanics model that can handle large deformations. In the present work, a fully coupled thermo-mechanical and meshfree approach, based on the momentum-consistent smoothed particle Galerkin (MC-SPG) method, is adapted and employed to predict wear of colliding asperities. The MC-SPG-based approach is used to study how plastic deformation, thermal response, and wear are influenced by the variation of the vertical overlap between colliding spherical asperities. The findings demonstrate a critical overlap value where the wear mechanism transitions from plastic deformation to brittle fracture. In addition, the results reveal a linear relationship between the average temperature and the increasing overlap size, up until the critical overlap value. Beyond this critical point, the average temperature reaches a steady-state value.

The Finite Element Method of High Degree of Accuracy for Boundary Value Problem with Singularity

Mathematical models of fracture physics and mechanics are boundary value problems for differential equations and systems of equations with a singularity. There are two classes of problems with a singularity: with coordinated and uncoordinated degeneracy of the input data, depending on the behavior of the coefficients of the equation. Finite element methods with the first order of convergence rate O(h) have been created to find an approximate solution to these problems. We construct a scheme of the weighted finite element method of high degree of accuracy for the boundary value problem with uncoordinated degeneracy of the input data and singularity of the solution. The rate of convergence of an approximate solution of the proposed finite element method to the exact Rν-generalized solution in the weight set W2,ν+β2+21(Ω,δ) is investigated. The estimation of finite element approximation O(h2) is established.

Toughening amplification of microcracks in staggered composites

Biological materials depict an excellent combination of both strength and toughness, which is a vital requirement for most engineering materials. It provides motifs to revolutionize the techniques for producing novel materials with improved properties. However, there is still a lack of deep understanding regarding the toughening mechanisms in biological materials, in order to overcome the conflict between strength and toughness in synthetic materials. This paper establishes a microstructure-based fracture model to reveal the toughening effect of the microcrack zone near the crack tip. Firstly, the stress–strain relationship considering the initiation and saturation of microcracks is derived. Then, a fracture mechanics model incorporating the micro-mechanics of microcracks is established, based on the above nonlinear mechanical response. Finally, the model is used to investigate the influence of microstructural parameters on the fracture toughness considering microcracks. The results show that there are two nondimensional parameters that significantly influence the fracture toughness: the ratio between the gap and overlapped zone, ξ, and λla. In addition, the selection of the microstructural parameters not only needs to consider the balance between stiffness, strength, and toughness, but also achieve the optimal toughness by combining the effects of several different mechanisms.

A multiscale nonlinear fracture model for staggered composites to reveal the toughening effect of process zone

The attainment of both strength and toughness is a vital requirement for most structural materials. Unfortunately, these properties are generally mutually exclusive in synthetic materials. Natural structural materials defeat the conflict of strength versus toughness, and provide design motifs for the high-performance materials. However, there still lacks a deep understanding of the toughening mechanisms in bioinspired composites. This paper presents a microstructure-based nonlinear fracture mechanics model for staggered composites, to investigate the toughening effect of the nonlinear deformation in the process zone. Firstly, a nonlinear stress–strain relationship of staggered composites is derived, to capture the plastic deformation of the matrix. Then, a multiscale nonlinear fracture mechanics model incorporating the effect of crack bridging and process zone is established based on the above constitutive relation and HRR theory. Finally, the model is used to reveal the influence of geometric and constitutive parameters. The results demonstrate that the process zone leads to a tremendous contribution to the overall toughness. And the crack resistance curve is rising with crack extension due to the increase of the process zone. What is more, there still exists an optimal balance between toughness, stiffness, and strength in biological materials. These results can provide guidelines for the design of high-performance composites.

Extracting the 3D spatial structure of soil cracks in the North China Plain from paraffin casting and exploring the developmental patterns of vertical cross-sectional morphology of the cracks

Cracking from soil desiccation is a common phenomenon. Understanding the structure of cracks is highly important in the research of soil moisture and heat transportation, as well as the strength of soil structure within soil. There is limited research on the three-dimensional (3D) spatial characteristics of soil desiccation cracks. Furthermore, the absence of a dependable and precise in-situ technique for extracting and digitizing the three-dimensional crack structure means that the commonly employed simplified crack models (such as V-shaped and cuboid-shaped) have received limited testing. This study examines the feasibility of extracting the 3D structure of cracks by combining in-situ paraffin casting in sandy loam soil of North China Plain with a 3D laser scanner. Parameters (length (L), width (W), depth (D), depth to width ratio (C)), as well as the vertical cross-section profile (W ∼ D) of each crack, were used to quantitatively describe the structure of cracks. Our study demonstrated that digitalized 3D cracks with 5 μm spatial resolution can be obtained quickly by paraffin infusion combined with a 3D laser scanner. Our result based on 18 crack cross-section profiles also demonstrates that W ∼ D do not follow either the V-shaped crack model or the cuboid-shaped crack model. All of the 18 normalized vertical profiles of cracks obey the power function relationship (R2 = 0.850) rather than the linear relationship of the V-shaped model (R2 = 0.794). The shape of the soil moisture profile is convex, which contradicts the concave profile of the observed vertical cracks. Even after combining the Soil Shrinkage Characteristic Curve (SSCC) with the soil moisture profile, we still failed to replicate the observed concave crack profile. The observed crack morphology in experiments can be replicated by both the elliptical model and the parabolic model of fracture mechanics, albeit with less predictive accuracy when compared to the power function model. This suggests that the current understanding of soil desiccation cracking in soil science is deficient, as it lacks appropriate methods and theoretical mechanisms for investigating soil cracking.

Coupled versus energetic nonlocal failure criteria: A case study on the crack onset from circular holes under biaxial loadings

The phenomenon of brittle crack onset stemming from a circular hole in an infinite plate subjected to remote biaxial loading is herein investigated. A thorough analysis on the influence of the loading biaxiality reveals the existence of a wide casuistry in the sign and trend distributions of the stress field and Stress Intensity Factor, thus rendering it an exhaustive case study for assessing different failure criteria. Subsequently, three different approaches are used to determine the biaxial safety domains, two of which rely on the coupling of stress and energy conditions for failure, namely Finite Fracture Mechanics and Cohesive Zone Model, plus the purely energy-driven Phase Field model of fracture. Noteworthy, Finite Fracture Mechanics predicts the existence of a region in the loading space where failure is exclusively governed by the energy condition. Likewise, it is mathematically proven that the system of equations governing Dugdale's Cohesive Zone Model is equivalent to the first-order minimization condition of the energy balance, the resultant predictions being fairly close to those obtained by Finite Fracture Mechanics. Lastly, the Phase Field model of fracture is numerically implemented in the context of Finite Elements while paying special attention to the choice of the energy decomposition, whereof two are implemented: No-Decomposition and No-Tension decomposition. Specifically, the latter showcases satisfactory agreement with both Finite Fracture Mechanics and Dugdale's Cohesive Zone Model, thus posing a solid contender for studying complex fracture scenarios upon combined tension-compression stress states.

Preliminary study on the determination of the Weibull modulus of strength distribution in quasi-brittle materials

In this paper, how to determine the Weibull modulus of a fracture strength distribution is discussed with its physical implications for quasi-brittle materials. Based on the Markov chain assumption, it is shown that the lifetime (i.e., the time taken for formation of a critical defect) in a quasi-brittle material can be described by a gamma probabilistic distribution function. Prior to macroscopic failure, the effective number of energy barriers to be overcome is determined by the slope of the energy barrier spectrum, which is equivalent to the Weibull modulus. Based on a fracture mechanics model, the fracture energy barrier spectral slope and Weibull modulus can be calculated theoretically. Furthermore, such a model can be extended to take into account the crack interactions and defect-induced degradation. The predicted Weibull modulus is good agreement with that derived from available experimental results.

A Damage Constitutive Model for a Jointed Rock Mass under Triaxial Compression

Due to the different structural characteristics and in situ environment, jointed rock masses encounter different failure mechanisms. Because of the joints, jointed rock masses show peculiar characteristics such as anisotropy and weakening. To describe the deformation and failure mechanism in jointed rock masses, a novel damage constitutive model of rock mass is proposed here considering the geometric parameters and mechanical properties of joints. A total damage variable is derived on the basis of the strain equivalence hypothesis, which combines the Weibull statistical damage theory for the strength of the rock elements and the fracture mechanics model for joints. This new damage variable reflects the coupled damage inflicted by two damage states, one is initial damage induced by prefabricated joints and the other is joint damage and rock mesoscopic damage under loading. The damage evolution path revealed by the new damage variable corresponds to the evolution of mechanical properties and behaviors induced by changes in the rock mass structure. Afterward, the computational formulation scheme for the model parameters is deduced using the extremum method. The model parameters, m and F0, have a clear physical meaning. The parameter m describes the ductility–brittleness characteristics of jointed rock masses, and F0 reflects the level of strength. This model describes the effect of joints and strain on the evolution of rock mass damage, model parameters, deformation, and failure characteristics. The mechanical behavior of rock mass described by the damage model and the change law of model parameters are consistent with the published experimental results.

Engineering Method for Calculating the Limiting Amplitudes of Stress Cycles for Structural Steels

In large-sized metal structures, various stress concentrators are often present, which affects the operation of the material. These are intermittent bonds, holes, welded joints, material defects, etc. As a result of overloads under the action of an external cyclic load on structures in the area of stress raisers, the cycle asymmetry, the level of maximum stresses and deformations increase. In this case, the determination of the limit values of the stress cycles can be performed using a diagram of the limit stress amplitudes. The paper presents an engineering method for calculating the limiting stress amplitudes and constructing Hay’s diagrams. It is based on the use of mathematical models of classical linear and structural-mechanical fracture mechanics. Analytically and by calculation, the validity of the method is shown, which consists in determining the endurance limits and limiting stress amplitudes under high-cycle loading in a wide range of variation of the cycle asymmetry coefficient for ferrite-pearlite steels with a yield strength of up to 400 MPa. Thus, a generalized calculation method has been developed for determining the endurance limits for high values of cycle asymmetry and cycle stresses. The error of the method is estimated in the area of low-cycle load. The influence of constant and average load in a cycle on the endurance limit has been investigated both for high-cycle and low-cycle loading. The proposed approach allows to construct Smith and Hay’s fatigue diagrams for the tensile region, taking into account the structural characteristics of the material and the error allowed for engineering calculations.

A generalized machine learning framework for brittle crack problems using transfer learning and graph neural networks

Despite their recent success, machine learning (ML) models such as graph neural networks (GNNs), suffer from drawbacks such as the need for large training datasets and poor performance for unseen cases. In this work, we use transfer learning (TL) approaches to circumvent the need for retraining with large datasets. We apply TL to an existing ML framework, trained to predict multiple crack propagation and stress evolution in brittle materials under Mode I loading. The new framework, ACCelerated Universal fRAcTure Emulator (ACCURATE), is generalized to a variety of crack problems by using a sequence of TL update steps including (i) arbitrary crack lengths, (ii) arbitrary crack orientations, (iii) square domains, (iv) horizontal domains, and (v) shear loadings. We show that using small training datasets of 20 simulations for each TL update step, ACCURATE achieved high prediction accuracy in Mode-I and Mode-II stress intensity factors, and crack paths for these problems. We demonstrate ACCURATE’s ability to predict crack growth and stress evolution with high accuracy for unseen cases involving the combination of new boundary dimensions with arbitrary crack lengths and crack orientations in both tensile and shear loading. We also demonstrate significantly accelerated simulation times of up to 2 orders of magnitude faster (200x) compared to an XFEM-based fracture model. The ACCURATE framework provides a universal computational fracture mechanics model that can be easily modified or extended in future work.

Size‐scale effects in high‐performance reinforced and prestressed concrete T‐beams

AbstractReinforced concrete (RC) and prestressed concrete (PC) structural elements need to be designed in order to guarantee large plastic deformations, avoiding any loss in their load bearing capacity. In this framework, the rotation capacity of RC and PC beams has been demonstrated to be a function of concrete mechanical properties, reinforcement characteristics, and of the structural size. On the other hand, Theory of Plasticity as well as the International Standards completely disregard size‐scale effects and ductile‐to‐brittle transitions, leading to an overlook of the strain‐softening behavior of the concrete matrix and of the rotation capacity of RC beams. On the other hand, the Cohesive/Overlapping Crack Model is able to evaluate concrete cracking in tension and concrete crushing in compression, as well as snap‐back and snap‐through unstable phenomena, steel yielding and/or slippage. This Nonlinear Fracture Mechanics model predicts a reduction in the moment versus rotation plastic plateau by increasing the beam depth and/or the reinforcement percentage. The numerical investigations carried out on reinforced and prestressed high‐performance concrete beams having rectangular or T‐shaped cross‐sections highlight the size‐scale effects on plastic rotation capacity that allow to formulate new scale‐dependent upper and lower limits of reinforcement percentage to guarantee a stable and ductile postpeak behavior of reinforced concrete structures.

Scale effects in GFRP‐bar reinforced concrete beams

AbstractGlass fiber‐reinforced polymer (GFRP)‐reinforced concrete (RC) can be defined as a cementitious material in which the reinforcing secondary phase consists in corrosion‐resistant GFRP rebars. For this next‐generation structural material, experimental flexural tests highlight how the postcracking response is strongly affected by the amount of GFRP area together with the structural size‐scale. In this work, the cohesive/overlapping crack model (COCM) is adopted to describe the transition between cracking and crushing failures occurring in GFRP‐RC beams by increasing the beam depth, the reinforcement percentage, and/or the concrete compression strength. Within this nonlinear fracture mechanics model, the tensile and compression ultimate behaviors of the concrete matrix are modeled through two different process zones that advance independently one of another. Moreover, this model is able to investigate local mechanical instabilities occurring in the structural behavior of GFRP‐RC beams: tensile snap back and snap‐through, which are due to concrete cracking and reinforcement bridging action, and the compression snap‐back generated by the unstable growth of the crushing zone. In this context, the application of the COCM highlights that the ductility, which is represented by the plastic rotation capacity of the GFRP‐RC beam only when the reinforcement can slip, decreases as reinforcement percentage and/or beam depth increase. In this way, rational and quantitative definitions of hyperstrength and brittle compression crushing behaviors can be provided as a GFRP percentage depending on the beam depth.

A Methodology for Stochastic Simulation of Head Impact on Windshields

In accidents involving cars with pedestrians, the impact of the head on structural parts of the vehicle presents a significant risk of injury. If the head hits the windshield, the injury is highly influenced by glass fracture. In pedestrian protection tests, a head form impactor is shot on the windshield while the resultant acceleration at the centre of gravity of the head is measured. To assess the risk of fatal or serious injury, a head injury criterion (HIC) as an explicit function of the measured acceleration can be determined. The braking strength of glass, which has a major impact on the head acceleration, however, is not deterministic but depends on production-related microcracks on the glass surface as well as on the loading rate. The aim of the present paper is to show a pragmatic method for how to include the stochastic failure of glass in crash and impact simulations. The methodology includes a fracture mechanical model for the strain rate-dependent failure of glass, an experimental determination of the glass strength for the different areas of a windshield (surface, edge, and screen-printing area), a statistical evaluation of the experimental data, and a computation of an HIC probability distribution by stochastic simulation.

Cohesive-zone based fracture mechanics model of an edge delamination in bimaterial beam under mixed-mode bending test

The problem of an edge-split bilayer beam consisted of bonded dissimilar materials under mixed-mode bending (MMB) is investigated by using a structural mechanics procedure. In this analytical procedure, the bilayer beam is modeled as two Timoshenko beams joined by using interface tensile and shear springs, and the fracture mechanics parameters including the strain energy release rate and phase angle are estimated from the spring responses. Numerical examples of bilayer beams consisted of isotropic or orthotropic bimaterials and with symmetric or asymmetric dimensions are presented and compared to continuum based finite-element solutions with either cohesive-zone or perfectly-bonded interface models. It is shown that the strain energy release rates obtained from these models are in good agreement. The phase angles obtained from the analytical model and the cohesive-zone-interface based continuum model are also consistent with each other, and agree to the crack-tip deformation. On the other hand, the phase angles obtained from the oscillating crack-tip fields related to the perfectly-bonded interface do not match to the crack-tip deformation as well as the cohesive-zone interface models. Consequently, it is recommended to characterize the mode-mixity dependent interfacial adhesion and fatigue responses by using the fracture mechanics parameters obtained by using the analytical solution for the MMB fracture problem.

Analysis on fracture mechanics theory of roof cutting instability mechanism with large mining height face in shallow coal seam

The roof in a fully-mechanized face of a shallow coal seam with large mining height is prone to form a combined cantilever—articulated rock beam structure. When the support resistance is insufficient, the articulated rock beam will sink. This will make the combined cantilever beam rotate and fracture. It is then easy to induce the sliding and instability of the articulated rock beam, which results in large-scale roof cutting and the support crushing. Taking the combined cantilever beam structure as the main research object, and considering the mining damaged characteristics of cantilever beam rock stratum, the rock beam was regarded as a finite plate model with an edge crack of arbitrary dip angle. In addition, a fracture mechanics model controlled by a set of structural planes was established, the instability conditions of rock beam and the main control factors were analyzed, and the method of determining the support resistance were discussed. The results show that the cantilever beam rotates and fractures. This causes a chain reaction of the rock beam that leads to fracture. The combined cantilever beam then loses stability with the increase of the length of the crack length and the crack dip angle, and therefore it is easier to penetrate the cantilever beam and cause roof instability. The necessary condition for rock beam instability was crack activation, and the sufficient condition was the airfoil branch crack propagate through the rock beam. The influence degree of each parameter on the support resistance was thus determined: crack length a > crack dip angle β > rock thickness h > weighting interval l. The theoretical analysis results were proven to be reasonable by an in situ monitoring example of no. 22,310 working face in the Daliuta coal mine, China. On this basis, the reasonable value of support resistance was obtained. The conclusions of this research provide a new method for researching the roof instability mechanism. They are also conducive to the green and sustainable development of mines.

Experimental research on influence mechanism of loading rates on rock pressure stimulated currents

The study of pressure stimulated current (PSC) changes of rocks is significant to monitor dynamic disasters in mines and rock masses. The existing studies focus on change laws and mechanism of currents generated under the loading of rocks. An electrical and mechanics test system was established in this paper to explore the impacts of loading rates on PSCs. The results indicated that PSC curves of different rocks had different change laws under low/high loading rates. When the loading rate was relatively low, PSC curves firstly changed gently and then increased exponentially. Under high loading rates, PSC curves experienced the rapid increase stage, gentle increase stage and sudden change stage. The compressive strength could greatly affect the peak PSC in case of rock failure. The loading rate was a key factor in average PSC. Under low loading rates, the variations of PSCs conformed to the damage charge model of fracture mechanics, while they did not at the fracture moment. Under high loading rates, the PSCs at low stress didn’t fit the model due to the stress impact effects. The experimental results could provide theoretical basis for the influence of loading rates on PSCs.

Machine visual technology based steel corrosion evaluation and analysis of power transformation lines: A Zhejiang power grid case study

It can be seen that the corrosion failure of transmission and transformation equipment has increasingly restricted the safe operation of the Zhejiang power grid bottleneck problem. If effective anticorrosion measures are not taken promptly, transmission and transformation equipment serving in various sophisticated atmospheric environments will suffer serious corrosion damage in a relatively short period, which endangers the safe usage of transmission and transformation equipment and the security of grid operation. In this article, through the establishment of transmission and transformation steel components corrosion fracture mechanics model, a standard corrosion spectrum grading software based on DeepLabV3+ image segmentation technology is developed to determine the quantitative assessment method of corrosion damage and assess the corrosion status with safety degree of transmission and transformation equipment. According to the assessment results, the operation and maintenance units are guided to adopt differentiated corrosion maintenance and replacement strategies, so as to reduce corrosion safety hazards and reduce safety accidents and economic losses caused by corrosion, which is of great significance for the safe operation of power grids.

Swelling induced debonding of thin hydrogel films grafted on silicon substrates.

We report on the delamination of thin (≈μm) hydrogel films grafted to silicon substrates under the action of swelling stresses. Poly(dimetylacrylamide) (PDMA) films are synthesized by simultaneously cross-linking and grafting preformed polymer chains onto the silicon substrate using a thiol-ene reaction. The grafting density at the film/substrate interface is tuned by varying the surface density of reactive thiol-silane groups on the silicon substrate. Delamination of the films from well controlled line defects with low adhesion is monitored under a humid water vapor flow ensuring full saturation of the polymer network. A propagating delamination of the film is observed under the action of differential swelling stresses at the debonding front. A threshold thickness for the onset of this delamination is evidenced which is increasing with grafting density while the debonding velocity is also observed to decrease with an increase in grafting density. These observations are discussed within the framework of a nonlinear fracture mechanics model which assumes that the driving force for crack propagation is the difference between the swelling state of the bonded and delaminated parts of the film. Using this model, the threshold energy for crack initiation was determined from the measured threshold thickness and discussed in relation to the surface density of reactive thiol groups on the substrate.

Residual stress effects on fatigue crack growth in different regions of aluminum alloy 7050 friction stir weld

AbstractDifferent distribution of residual stress in each microregion of the joint had an intensely significant influence on the fatigue crack growth. The friction stir welding (FSW) finite element model was developed. The residual stress was imported to the fracture mechanical model by the submodel technique. The residual Krs (stress intensity factor from residual stress) approaches were used to predict the fatigue crack growth rate (FCGR) in different regions of aluminum alloy 7050 friction stir welded joints. The FRANC3D in conjunction with ABAQUS, the M‐integral method was used to calculate Krs, considering the effect of Krs on the effective stress ratio, the Paris–Walker formula was used to predict the FCGR in different regions of the FSW joints. The predicting results and experimental values aligned with the better, demonstrating that the established model could accurately predict the FCGR in different regions of the FSW joints.

Uniform fatigue damage tolerance assessment for additively manufactured and cast Al-Si alloys: size and mean stress effects

• Influence of additively manufacturing and casting on microstructure and porosity characteristics as well as quasi-static and cyclic stress-strain behavior of Al-Si alloys • Linear-elastic (LEFM: Murakami, Murakami-Schijve) and elastic-plastic fracture mechanics (EPFM: Fischer) were used for determination of stress intensity factor at failure-initiating defect and plotted in Shiozawa diagrams • LEFM and EPFM enables to consider the size effect within fatigue damage tolerance assessment • Benchmark of Woehler, Murakami, Murakami-Schijve and Fischer approaches for fatigue damage tolerance assessment regarding size effect and mean stress effect, whereby only Fischer approach enables a uniform fatigue damage tolerance assessment The near-net-shape manufacturing in additive manufactured and cast of Al-Si alloys results in a heterogeneous solidification and cooling of the parts, leading to significant gradients in microstructural and defect features as well as deformation behavior. In this paper, an elastic-plastic fracture mechanical model for uniform fatigue damage tolerance assessment of Al-Si alloys was further qualified and extended for a uniform view of different testing volumes as well as various stress ratios between R = -2…0.5 based on the fracture mechanical approaches of Murakami (√area) and Shiozawa for a reliable main crack defect-based mechanical design of fatigue-loaded structures. The linear-elastic fracture mechanical (LEFM) approaches of Murakami, Murakami-Schijve and Shiozawa were used to calculate defect-based lifetime curves, where the cyclic stress intensity factor (ΔK) at the failure-initiating defect (√area) was used to describe the local stress concentration conditions (so-called K-N curves) instead of nominal stress-based S-N curves. The LEFM-based K-N curves did not allow a unified assessment of fatigue behavior. Therefore, the cyclic stress-strain (CSS) behavior (K’, n’) was used for a plasticity-modification of the LEFM approach based on the elastic-plastic fracture mechanical (EPFM) approach of Fischer by calculating the effective cyclic J integral (ΔJ eff ) to plot J-based K-N curves, called Kj-N curves. This EPFM approach could be qualified for a uniform and reliable fatigue damage tolerance assessment of AM and sand cast Al-Si alloys for the HCF regime.