Fracture Of Materials Research Articles

Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures

Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely beyond reach. In this work, we propose a learning framework to extract a peridynamics model as a mesoscale continuum surrogate from MD simulated material fracture data sets. Firstly, we develop a novel coarse-graining method, to automatically handle the material fracture and its corresponding discontinuities in the MD displacement data sets. Inspired by the weighted essentially non-oscillatory (WENO) scheme, the key idea lies at an adaptive procedure to automatically choose the locally smoothest stencil, then reconstruct the coarse-grained material displacement field as the piecewise smooth solutions containing discontinuities. Then, based on the coarse-grained MD data, a two-phase optimization-based learning approach is proposed to infer the optimal peridynamics model with damage criterion. In the first phase, we identify the optimal nonlocal kernel function from the data sets without material damage to capture the material stiffness properties. Then, in the second phase, the material damage criterion is learnt as a smoothed step function from the data with fractures. As a result, a peridynamics surrogate is obtained. As a continuum model, our peridynamics surrogate model can be employed in further prediction tasks with different grid resolutions from training, and hence allows for substantial reductions in computational cost compared with MD. We illustrate the efficacy of the proposed approach with several numerical tests for the dynamic crack propagation problem in a single-layer graphene. Our tests show that the proposed data-driven model is robust and generalizable, in the sense that it is capable of modeling the initialization and growth of fractures under discretization and loading settings that are different from the ones used during training.

Sub-millisecond 4D X-ray tomography achieved with a multibeam X-ray imaging system

A proof-of-concept experiment for sub-millisecond temporal and 10 μm order spatial resolution 4D X-ray tomography imaging using a multibeam X-ray imaging system is reported. The 3D structure of a tungsten wire during mechanical deformation was reconstructed using a super-compressed sensing-based algorithm from 28 projection images acquired simultaneously with a temporal resolution of 0.5 ms. The multibeam imaging system does not require rotation of the sample, X-ray source or detector. The experiment demonstrates the potential for improving the time resolution in observing non-repeatable dynamic phenomena, such as those occurring in fluids, living beings, or material fractures.

A unifying finite strain modeling framework for anisotropic mixed-mode fracture in soft materials

A unifying finite strain modeling framework for anisotropic mixed-mode fracture in soft materials

Numerical fatigue modeling and simulation of interacting surface cracks in offshore wind structural connections

The structural integrity of marine structures is significantly influenced in many practical applications by their fatigue behavior, especially when dealing with dynamically sensitive structural systems, e.g., offshore wind substructures. The propagation of cracks found in structural components can be estimated through fracture mechanics-based methods, in which the crack growth under cyclic loading is mainly driven by the stress intensity factor (SIF). To simplify the computation of the SIF, closed-form solutions are often suggested in industrial standards, yet their applicability is limited to specific geometries and loading conditions. Overcoming the aforementioned constraints, we propose here a general methodology for numerically simulating the SIF and growth of multiple cracks by computing the SIF of adjacent cracks in an integrated finite element analysis, in which interaction effects are implicitly considered. In our proposed method, the coalescence of bordering cracks is also adequately modeled and fatigue failure is defined based on fracture mechanics principles. With the objective of enabling an efficient SIF computation, we also provide the necessary modeling details for the appropriate implementation of the corresponding finite element analysis. The proposed methodology is then tested and validated in a finite thickness plate under cyclic loading setting, whereas in a more practical case study, we investigate the fatigue analysis of interacting surface cracks in an offshore wind structural connection. The results emphasize the importance of considering interaction effects and crack coalescence when simulating the fatigue evolution of structural details in practical applications, and within the study, specific insights are additionally provided for the fatigue analysis of offshore wind structural components. With respect to the investigated fatigue failure criteria, the results show that a through-thickness limit state might yield slightly conservative fatigue life estimates compared to the fatigue limit that results when failure is defined based on the material fracture toughness.

Patterns of localized deformation at pre-fracture stage in carbon steel – stainless steel bimetal

The work is devoted to the study of strain localization at macroscale level during parabolic mechanical hardening and pre-fracture under quasi-static loading of a carbon steel – stainless steel bimetal. The problem of estimating the scale of the phenomena that determine plasticity is decisive in the development of any theories of plastic deformation, in particular, dislocation theories. The main difficulty in constructing such theories is the reconciling the dislocation scales, characteristic for most deformation and mechanical hardening mechanisms, with macroscopic parameters of deformation processes. In the framework of the autowave model of localized plastic deformation, this problem can be reduced to the possibility of obtaining parameters from the results of macroscale observations of localized plastic flow development. During the experiments, it was confirmed that in a bimetal at any forming stage, a specific pattern of localization centers distribution is spontaneously generated - a pattern of localized plastic flow. The shape of such patterns is determined by the law of mechanical hardening acting in the material. It is shown that the observed localization patterns can be used as an informative feature in predicting the plasticity margin. In the process of uniaxial tension at the stage of parabolic mechanical hardening of the bimetal, the deformation mode is realized with the formation of several potential fracture centers. It was established that at the pre-fracture stage, during the time evolution of the wave pattern of deformation localization, the zone of active plastic deformation narrows, but the number of centers in it either remains the same with a decrease in the distance between them, or even increases. The result of this process is the formation of a macroscopic neck, and then fracture. At the pre-fracture stage, the collapse point indicates the place of future fracture and signals the need to stop the deformation process in order to avoid the fracture of the bimetallic material. Thus, the well-known manifestation of deformation macroscopic localization – formation of a neck – is preceded by complex phenomena of mutually coordinated motion of localized plasticity centers at the pre-fracture stage.

On the use of strength criteria of anisotropic materials

One of the distinctive properties of composite materials is their anisotropy, which allows, in particular, to use of their strength properties maximum. Thanks to new technologies, in particular 3-D printing, there are new opportunities for purposeful formation of the structure of composite materials and their properties. An important issue here is ensuring strength, which is determined depending on the structure of the composite as a whole and the mechanical characteristics of its individual components. The article reviews well-known strength criteria (Goldenblatt-Kopnov, Mises-Hill, Fisher, Hoffman, Tsai-Wu, and others), the relationship between them, and data on the reliability of their application under certain load conditions. Some of them assume the same properties of materials under conditions of compression and tension and are obtained by generalizing the classical theories of strength and plasticity of isotropic bodies. The criteria that take into account the different resistance of the composite material to tension and compression, which is inherent in many composite materials, have gained greater practical application. When choosing a strength criterion, from the point of view of structure, it is worth considering separately layered and reinforced composite materials, and from the point of view of load - the static or cyclic nature of its application. The criteria listed above do not take into account the damage accumulation in the material that occurs under the influence of external loads. The number of such known criteria is limited, because today there is no method for predicting the stage of scattered fracture of composite materials taking into account the anisotropy of mechanical properties, and the choice of the damage parameter is not justified. The perspective of developing such criteria for clarifying the received conclusions regarding the load-bearing capacity of products made of composite materials under different types of application of external loads is noted.

Tunable three-dimensional architecture of nematic disclination lines

Disclination lines play a key role in many physical processes, from the fracture of materials to the formation of the early universe. Achieving versatile control over disclinations is key to developing novel electro-optical devices, programmable origami, directed colloidal assembly, and controlling active matter. Here, we introduce a theoretical framework to tailor three-dimensional disclination architecture in nematic liquid crystals experimentally. We produce quantitative predictions for the connectivity and shape of disclination lines found in nematics confined between two thinly spaced glass substrates with strong patterned planar anchoring. By drawing an analogy between nematic liquid crystals and magnetostatics, we find that i) disclination lines connect defects with the same topological charge on opposite surfaces and ii) disclination lines are attracted to regions of the highest twist. Using polarized light to pattern the in-plane alignment of liquid crystal molecules, we test these predictions experimentally and identify critical parameters that tune the disclination lines' curvature. We verify our predictions with computer simulations and find nondimensional parameters enabling us to match experiments and simulations at different length scales. Our work provides a powerful method to understand and practically control defect lines in nematic liquid crystals.

The coupling effects of strain gradient and damage on Mode I crack tip stress fields

The cleavage fracture of metallic materials is determined by the crack tip stress field depending on plastic strain gradient and microstructural damage. The synergistic effects of strain gradient and damage on the stress fields near a Mode I crack tip in metallic materials are investigated using a modified conventional theory of mechanism-based strain gradient plasticity (CMSG). Besides preserving the essence of classical CMSG, a stress-dependent damage variable is introduced to characterize the effect of microstructural damage on the material's intrinsic length, elastic modulus and plastic yielding criterion. Based on the present theoretical model, it is found that the strain gradient and microstructural damage effects both are prominent in a small region near the Mode I crack tip, at which the damage evolution is determined by the strain gradient. Although the crack tip stress field with strain gradient and damage effects is lower than the existing ones influenced only by strain gradient, it is still significantly higher compared with the yielding strength of the material so that the cleavage fracture at the crack tip can be well explained. The damage-induced stress level reduction indicates that the stress concentration at the crack tip can be alleviated to inhibit the crack propagation. As a result, when the damage effect is considered, not only a larger external load is required to induce crack propagation but also the plastic region in front of the crack tip is enlarged, consequently leading to increases of fracture strength and energy dissipation in the material. The present research provides a more precise prediction of the crack tip stress distribution in metallic materials, which is helpful for better understanding the microscopic mechanism of the cleavage fracture phenomenon.

Determination of fracture toughness and yield strength of Inconel 718 by milling operation

This paper presents an analytical scheme to determine the fracture toughness and the yield strength of Inconel 718 by the widely used milling operation. It is noted that there exists material fracture at the tool tip and the removed layer of material undergoes plastic deformation along the primary shear plane. The fracture toughness is considered at the tool tip and the yield strength is applied on the primary shear plane. Subsequently, the modified Williams’ model and the modified Williams-minimization model are both proposed on the basis of the geometries and mechanics in the oblique cutting process. The modelling framework indicates that milling can be developed as an alternative method to determine the fracture toughness and the yield strength from the serrated chip thicknesses combined with the corresponding cutting forces. This is because the experimental method by milling is a convenient scheme as it only requires the cutting forces per unit width of cut with respect to a series of uncut chip thicknesses. In addition, the normal shear angle is predicted by applying the principle of energy minimization. Finally, milling experiments are conducted to validate the two proposed methods. Results show that the two analytical methods return similar values of fracture toughness and yield strength, respectively. Besides, it is noted that high values of yield strength are achieved based on Tresca criterion, which would indicate work hardening in the primary shear zone during the serrated chip formation. The proposed methods exhibit advantages of convenience and generality to derive the fracture toughness and the yield strength, since it is still a challenge for the traditional standard mechanical tests for Inconel 718 due to its toughness and ductility.

Customizing the morphology and microstructure of single-crystalline Ni-rich layered cathode materials for all-solid-state batteries

A single-crystalline Ni-rich cathode material is synthesized for high-performance all-solid-state batteries (ASSBs). We customize the morphology and microstructure of the material by optimizing the synthesis process (particle size control and post-heat treatment) and demonstrate the advantages of single-crystalline cathode materials for practical use in ASSBs. The particle density and particle hardness of single-crystalline cathode materials with a particle size of 5 μm are considerably higher than those of the conventional polycrystalline cathode materials that are composed of spherical aggregates of submicron-scale primary particles. These structural features of the single-crystalline cathode materials improve the long-term cycling performance and rate capability of an ASSB configured with an argyrodite–Li6PS5Cl solid electrolyte. This is mainly attributed to the intimate interfacial solid–solid contacts and enhanced diffusion kinetics induced by the monolithic morphology of the single-crystalline cathode materials in the electrode. Moreover, undesirable microcrack formation and particle fracture in cathode materials are effectively suppressed during cycling. The feasibility of ASSBs configured with single-crystalline Ni-rich cathode materials is examined in detail.

Quantifying the cohesive strength of rock materials by roughness analysis using a domain based multifractal framework

Cohesive strength or intrinsic tensile strength as well as cohesive length are two important unknowns for cohesive modelling of fracture and failure analysis of quasi-brittle materials including rocks. There is no direct method for measuring these parameters and their quantification is always challenging and controversial. In this study, a novel multifractal framework is employed to quantify the cohesive length of four different rock types including sandstone, marble, fine-grained granite and coarse-grained granite by analysing the roughness of their fracture surfaces in a wide range of length scales. On the one hand, microstructural heterogeneities of rock material at small enough length scales will cause multifractality of the roughness of its fractured surface. On the other hand, this intrinsic heterogeneity together with extrinsic features including loading and environmental conditions as well as geometrical features including shape and size of a quasi-brittle specimen or structure are forming a fracture process zone (FPZ) in front of any stress concentrators before crack propagation. Therefore, it is proposed that locating the transition from multifractality to mono-fractality of a rough rock fractured surface using the employed statistical mechanics method leads to quantifying the effective length of FPZ of a sharp crack or the cohesive length. This length is quantified for the studied rocks ranging from 0.4 to 1.1 mm. Moreover, by employing the theory of critical distances, the cohesive strength σc of these rocks is also quantified ranging from 15 to 36 MPa.

The Application of Finite Element Method for Analysis of Cross-Wedge Rolling Processes-A Review.

The aim of this article is to review the application of the finite element method (FEM) to cross-wedge rolling (CWR) modeling. CWR is a manufacturing process which is used to produce stepped axles and shafts as well as forged parts for further processing on forging presses. Although the concept of CWR was developed 140 years ago, it was not used in industry until after World War 2. This was due to the limitations connected with wedge tool design and the high costs of their construction. As a result, until the end of the twentieth century, CWR tools were constructed by rolling mill manufacturers as they employed engineers with the most considerable experience in CWR process design. The situation has only changed recently when FEM became widely used in CWR analysis. A vast number of theoretical studies have been carried out in recent years, and their findings are described in this overview article. This paper describes nine research areas in which FEM is effectively applied, namely: the states of stress and strain; force parameters; failure modes in CWR; material fracture; microstructure modeling; the formation of concavities on the workpiece ends; CWR formation of hollow parts; CWR formation of parts made of non-ferrous materials; and new CWR methods. Finally, to show the potential of FEM on CWR modeling, a CWR process for manufacturing a stepped shaft used in car gearboxes is simulated numerically. This numerical simulation example shows that FEM can be used to model very complex cases of CWR, which should lead to a growing interest in this advanced manufacturing technique in the future.

Mechanical Behavior of Chain-Link Wire Nets under Pressure from a Warhead: Quasistatic Experiments and Simulations

Wire nets woven from high-strength steel wires have been used as applique armor against attack by short-range weapons. In this study, the mechanical behavior of chain-link wire nets under pressure from a warhead was investigated by quasistatic experiments and simulations. First, the new rig, the warhead device, and the wire nets were designed; pressure tests were conducted; and the deformation, fracture of the wire nets, and pressure force vs. displacement curves were obtained and analyzed. Then, the numerical approach and Finite element (FE) model were developed, considering the contacts between the steel wires in the inner connections, the contacts between the warhead and the mesh of the wire nets, and the fracture of the steel wire material. By comparison with the experimental data, the numerical approach and FE model are shown to be reliable in predicting the behavior of the wire nets under pressure from a warhead. Finally, the parameters of the wire net size and the mesh angles were further investigated by using the validated numerical approach and FE model, and suggestions for the initial design of the wire nets are discussed.

Fatigue Behavior of Polymer Encapsulated Graphene to Mitigate Interfacial Fatigue Damage

In applications such as flexible electronic devices, graphene, and other 2D materials are frequently in contact with stretchable polymeric substrates. The interface between 2D materials and polymers is dominated by weak van der Waals forces and can eventually degrade due to the frequent dynamic mechanical loads that these devices experience. This can lead to significant local delamination and shear fracture of the 2D materials. Using the polydimethylsiloxane (PDMS) encapsulation method, it is shown that the damage in graphene is significantly mitigated when it is capped during dynamic loading. To track the spread of damage in both encapsulated and nonencapsulated graphene, in situ, cyclic loading is performed. The fundamental process driving this substantial reduction in damage propagation in the 2D lattice is explained by the conventional shear lag model. It is also observed that softer PDMS substrate and capping layer completely mitigate the fatigue damage in graphene for 100 cycles at 10% applied fatigue strain.

Fracture Toughness and Fatigue Crack Growth Analyses on a Biomedical Ti-27Nb Alloy under Constant Amplitude Loading Using Extended Finite Element Modelling.

The human body normally uses alternative materials such as implants to replace injured or damaged bone. Fatigue fracture is a common and serious type of damage in implant materials. Therefore, a deep understanding and estimation or prediction of such loading modes, which are influenced by many factors, is of great importance and attractiveness. In this study, the fracture toughness of Ti-27Nb, a well-known implant titanium alloy biomaterial, was simulated using an advanced finite element subroutine. Furthermore, a robust direct cyclic finite element fatigue model based on a fatigue failure criterion derived from Paris' law is used in conjunction with an advanced finite element model to estimate the initiation of fatigue crack growth in such materials under ambient conditions. The R-curve was fully predicted, yielding a minimum percent error of less than 2% for fracture toughness and less than 5% for fracture separation energy. This provides a valuable technique and data for fracture and fatigue performance of such bio-implant materials. Fatigue crack growth was predicted with a minimum percent difference of less than nine for compact tensile test standard specimens. The shape and mode of material behaviour have a significant effect on the Paris law constant. The fracture modes showed that the crack path is in two directions. The finite element direct cycle fatigue method was recommended to determine the fatigue crack growth of biomaterials.

Dynamic tensile fracture of iron: Molecular dynamics simulations and micromechanical model based on dislocation plasticity

Molecular dynamics (MD) shows a difference in the mechanisms of fracture of iron under uniaxial and isotropic tension. Uniaxial tension leads to the formation of a complex dislocation structure in the bulk of material, which reduces the pore formation threshold and spall strength. Increase in temperature up to about 900 K suppresses increase in dislocation density during uniaxial tension, which leads to increase in the spall strength to the level close to the case of hydrostatic (isotropic) tension. This temperature-induced increase in dynamic tensile strength is rather unusual. Preliminary compression of material mimicking the shock compression prior to tension creates a defect structure, which reduces the spall strength during the following tension. The MD results of isotropic tension are used to model the material fracture dynamics on continuum level. The Bayesian approach to model calibration is used to identify the parameters of the fracture model. The parameterized fracture model describes well the MD results in the considered temperature range 300–1100 K. The fracture model with additional accounting of void initiation on initial defects of material is used to describe the experimental observations of the spall strength of iron over a wide range of strain rates. The simulation results for undeformed iron are in good agreement with the experimental values of the spall strength at strain rates greater than 4 × 105 s-1 and give overestimated values at lower strain rates. The results of calculations for precompressed iron describe well the spall strength over the entire range of strain rates indicating that accounting for the defect structure created by the shock compression prior to tension is critical for moderate strain rates.

Damage to fracture in offshore engineering materials under several stress states: Blowout preventer valve application

This contribution proposes a study of the mechanical behavior from damage to fracture of normalized and annealed samples of AISI 4340 steel. Besides, a numerical study in a security device of offshore industry is conducted. Experimental tests were initially performed on smooth and notched cylindrical specimens subjected to monotonic tension as well as on rectangular specimens subjected to pure shear and a combination of shear and tension loads. Such experimental tests were selected to observe different combinations of the stress triaxiality and the normalized third invariant concerning the stress state. The two types of heat treatments were considered to achieve different levels of ductility and verify their influence on the fracture mode of the alloy. The approach based on the second invariant of the deviatoric stress tensor ( J 2), with nonlinear isotropic hardening, is assumed to describe the mechanical behavior of the material in axisymmetric and three-dimensional numerical simulations. Finite elements simulations were carried out to analyze the performance of a simplified version of a mechanism of a blow-out preventer-BOP valve. The experimental and numerical curves of force versus displacement were compared, highlighting the effect of the stress triaxiality, the third invariant and calibration condition on the behavior of the material. The evolution of the equivalent plastic strain was plotted, and the fracture onset compared with its maximum value. The results show that the AISI 4340 alloy is highly dependent on the stress triaxiality and third invariant. Moreover, it can be concluded that different calibration conditions for the isotropic hardening curve can result in different levels of forces for the correct performance of the BOP in a critical situation.

Higher-order nonlocal operator theory for phase-field modeling of ductile fracture in elasto-plastic materials

In this work, we propose a novel approach based on the higher-order nonlocal operator for the phase-field modeling of ductile fracture in elasto-plastic materials. The present method introduces the total energy function consisting of the elastic, plastic, and fracture terms. The plasticity is coupled with the fracture through the degradation function which is applied to the tensile part of the elastic strain energy. The proposed higher-order nonlocal operator method brings several advantages over the original nonlocal operator method that requires only first-order terms. Moreover, the proposed method does not require the direct computation of kernel function or moment matrix derivatives. Therefore, this approach can improve the computational efficiency and simplify in implementation. The accuracy and effectiveness of the proposed method are demonstrated through various numerical examples, which have the ability to detect complex patterns of ductile fracture, such as crack propagation and plastic localization.

A bond-based peridynamics modeling of polymeric material fracture under finite deformation

We have developed a bond-based peridynamics model to study the fracture of polymer networks under finite deformation. Our approach is based on the Kuhn–Grün model of randomly jointed polymers with extensible chains, which allows the rupture of polymers through the chain scission mechanism. We introduced a novel mesoscale potential function that intrinsically incorporates an Arruda–Boyce type model into a nonlocal continuum framework with the purpose of modeling the mechanical response of general polymeric materials and the fracture of polymers. We have demonstrated through a series of numerical examples, both two-dimensional and three-dimensional, that the proposed model is robust and efficient in modeling crack growth in polymeric materials. The model is carefully validated with experimental data and numerical results obtained on the basis of existing continuum mechanics polymer models. We have shown that the proposed peridynamic model is accurate and stable in various configurations and loading modes, such as mode I and shear crack opening. In comparison to existing continuum polymer models and fracture modeling methods, our present technique has the advantages of being theoretically simple, rigorous, and computationally fast. The numerical results show that the nonlocal polymer model can easily capture the fracture process in polymeric materials without complex ad hoc modeling parameters under finite deformation, and it has the potential to become a convenient simulation tool for modeling the polymer failure process in the design and optimization of polymeric materials.

On crack propagation in weak geomaterials: Revisiting the superdislocation model in the context of hydraulic fracture

In this paper the problem of hydraulic fracture in elasto-plastic pressure sensitive material is analyzed. The superdislocation model is used to approximate the plastic deformations in the crack tip area. This model is employed to derive a new crack propagation condition based on the concept of effective fracture toughness. A parametric analysis supported by FEM simulations is conducted to verify the underlying assumptions of the superdislocation model and the resulting crack propagation condition. The results, obtained with the new crack propagation condition for the HF problem, are compared with those produced by a commercial geomechanical FEM package Elfen. The comparison proves the validity of the new crack propagation condition and the proposed modeling approach.