Fracture Behavior Of Materials Research Articles

Investigation of Hydrogen Transport Behavior in Polyethylene Terephthalate Membrane by Prolonged Hydrogen Exposure Treatments

Polyethylene terephthalate (PET) is one of the most used polymeric substances in production of packaging materials, fibers, textiles, coatings, and engineering materials. This paper elucidates the transport parameters of hydrogen gas through a PET membrane, which was selected to be a sufficiently permeable substrate for setting up an empirical strategy that aims at developing hydrogen barrier coatings. An examination of the structural degradation of PET by prolonged hydrogen exposure was performed. Hydrogen permeation tests were performed on a PET membrane with a thickness of 50 μm. To investigate the behavior of the material by prolonged hydrogen treatment, hydrogen-exposure experiments were carried out at a certain hydrogen pressure and time. Comparisons of the mechanical properties of the material were documented both before and after hydrogen exposure. A strong impact of comparatively transient hydrogen exposure on the mechanical and hydrogen transport properties of PET was observed. After 72 h of hydrogen exposure at 103 hPa and 300 K, the tensile strength decreased by 19%, the diffusion coefficients more than doubled, and material fracture behavior changed from ductile to distinctly brittle. This underlines the importance of developing effective hydrogen barrier coatings in case PET tubing is intended for use in hydrogen transport or storage.

Investigation of the Thickness Effects on Three‐Dimensional Fracture Toughness in Metallic Materials via the Phase‐Field Model

ABSTRACTWith the wide application of large wall‐thickness metallic structures in engineering, there has been a growing focus on the three‐dimensional fracture issues associated with these materials. This article uses the phase‐field model to investigate the impact of thickness on elastic–plastic metallic materials. Initially, the fracture toughness of metallic materials in three dimensions is calculated under elastic deformation. The findings reveal that the outcomes obtained from the phase‐field model remain consistent regardless of thickness, thus confirming its effectiveness. Subsequently, the study delves into the three‐dimensional fracture behavior of metallic materials during plastic deformation. It illustrates how the phase–field model approach enables a thorough simulation of crack propagation within these materials, offering a comprehensive understanding of their fracture behavior. By analyzing the phase‐field contour, the thickness effects of three‐point bending specimens during crack growth are effectively captured. In addition, the dimensionless fracture toughness ratio trends with thickness are compared between phase‐field modeling and experimental results in the open literature, showing good agreement.

Mechanical properties and fracture behavior of sandstone similar materials with different joint positions and thicknesses based on triaxial testing and PFC simulation

The mechanical properties and failure characteristics of joined rocks have an important impact on the disaster prevention of underground engineering and the sustainable development of mineral resources. The effects of confining pressure, joint location, and joint thickness on the mechanical properties of rock-like specimens under triaxial test have been studied. Furthermore, using the "DFN-age" function of PFC numerical simulation, the stress characteristics, and failure characteristics of rock specimens under different confining pressure, joint location and joint thickness are analyzed. The research results indicate that as the thickness of the joint increases and the joint position approaches the center of the specimen, the compressive strength of the specimen decreases. As the confining pressure increases, the compressive strength increases and failure modes of rock like specimens with different joint types also tend to be similar. The specimens manifest complex shear-tensile composite failures. In addition, the initiation cracks and main control cracks at the joint terminus can be classified as reverse tensile wing cracks, reverse shear cracks, shear cracks and tensile wing cracks. When the joint thickness of the specimen is 1.0 mm and the distance from the joint position to the center of the specimen is 10–20 mm, the crack evolution characteristics and stress distribution law of the specimen will undergo a transformation.

Stochastic Extension of Nonlocal Macro–Mesoscale Consistent Damage Model for Fracture Behaviors of Concrete Materials

The nonlinearity and randomness in composite materials such as concrete present challenges regarding the safety analysis and reliability-based design of structures. Based on two-scale damage evolution and physically based geometry–energy conversion, the nonlocal macro–mesoscale consistent damage model (NMMD) shows a unique capability in dealing with the nonlinearity of crack evolution. In this paper, a stochastic extension of the NMMD model is proposed to analyze the stochastic fracture behaviors of concrete materials. The extended model uses the stochastic harmonic function (second kind) to represent the spatial variability in concrete properties and thus to investigate the influence of inhomogeneity in the cracking process. Numerical examples of three-point bending beams without defects and with initial cracks of various sizes demonstrate that the stochastic NMMD model is capable of not only capturing uncertain fluctuations in peak load but also simulating the random walk of the crack path with the instantaneous transition of fracture modes, as observed in experiments. In addition, the effectiveness of the stochastic NMMD model with only a single random field (i.e., Young’s modulus) also contradicts the conventional assertion that stochastic simulations of quasi-brittle fracture should contain at least two mechanical properties with spatial randomness. Finally, the investigation of fracture energy with stochastic fluctuations reveals that randomness resulting from heterogeneity can statistically improve the fracture toughness of concrete materials to some extent.

Phase field fracture in elastoplastic solids: a stress-state, strain-rate, and orientation dependent model in explicit dynamics and its applications to additively manufactured metals

Phase field models have gained growing popularity in analysing fracture behaviour of materials. However, few have been explored to simulate dynamic ductile fracture to date. This study aims to develop a phase field framework considering strain rate, stress state, and orientation dependent ductile fracture under dynamic loading. Firstly, governing equations of displacement and phase fields are formulated in an explicit finite element framework. Secondly, constitutive relations are established with a hypoelastic-plasticity framework, encompassing the influence of material orientation and strain rate on both plasticity and fracture initiation. Stress states dependent fracture initiation is also considered. Thirdly, finite element implementation and corotational formulation for constitutive equations are derived. To validate the proposed model, finally, additively manufactured samples, involving material-level and crack propagation specimens are tested under dynamic loading conditions. Overall, the proposed phase field model can properly reproduce the experimental force-displacement curves and crack paths. Uniaxial tension tests reveal that a higher strain rate can lead to a higher hardening curve and lower ductility. Other material specimens further demonstrate the capability to predict stress state and orientation dependent dynamic fracture. To simulate dynamic crack paths accurately, it is necessary to consider anisotropic fracture initiation. Lastly, the phase field model was applied for the first time to predict the dynamic response of triply periodic minimal surface (TPMS) structures. Dynamic crack patterns were effectively captured, and the fracture mechanisms were thoroughly analysed. This study provides an explicit phase field framework for dynamic ductile fracture, with applications to additively manufactured materials and structures.

A new adaptive peridynamic framework for modeling large deformation and fracture behavior of hyperelastic materials

Accurate prediction of deformation and fracture behaviors of hyperelastic materials is crucial in engineering applications and industry. The paper presents a new three-dimensional computational model to simulate large deformations and fractures in hyperelastic materials using the peridynamic method. The main innovation of the proposed three-dimensional hyperelastic peridynamic (3D-HPD) model lies in its incorporation of the stress–strain relationship of hyperelastic materials into the peridynamic framework. Therefore, the peridynamic parameters, such as bond stiffness and strength, are dynamically updated based on the instantaneous value of Young's modulus derived from the stress–strain relation of hyperelastic materials. The 3D-HPD model highlights the following novelties: 1) The 3D-HPD model directly employs the stress–strain relation for each peridynamic bond. Thus, the large deformations and fractures in hyperelastic materials are accurately captured in three dimensions by integrating the responses in all peridynamic bonds; 2) Unlike other models that may require specific hyperelastic formulations, the 3D-HPD model offers a more straightforward application, enhancing usability and reducing complexity; 3) The 3D-HPD model is capable of simulating the response of hyperelastic materials under various loading conditions, including tensile, torsional, and lateral loadings. We confirm the validity of the 3D-HPD model by evaluating it against experimental measurements and observations. For the first time, the model examines hyperelastic materials' fracture and deformation behaviors under combined loading conditions. The new findings of the mechanical performance of hyperelastic materials under multi-axial stresses provide new insights to enhance their design and usage.

Experimental and numerical investigation on ductile fracture of Q235 cold-formed thin-walled steel

In order to simulate the full-range moment-rotation characteristic of steel storage rack beam-to-upright connections incorporating material fracture, this paper presents experimental and numerical investigations into the fracture behaviour of Q235 cold-formed thin-walled steel (CFTWS) flat and corner materials. A total of 43 specimens derived from Q235 CFTWS plates were tested. Two different thicknesses (1.8 mm and 3.25 mm), three varied bend angles (0°, 70° and 90°), and five types of specimens representing different stress states, were considered. The load-displacement curves and fracture characteristics of each specimen were derived from tests. The refined numerical models were established and validated by the test data. Based on experimental and numerical simulation results, four commonly used ductile fracture models for metal materials were calibrated and compared. The results show that the verified LMVGM fracture model is applicable to Q235 CFTWS flat and corner materials, and then compiled into a USDFLD subroutine in numerical simulation models to predict the flexural behaviour of storage rack beam-to-upright connections. The comparison between test and numerical simulation results illustrates that the established ductile fracture model for Q235 CFTWS materials can accurately simulate the fracture related failure modes of beam-to-upright connections in CFTWS storage racks.

Uncoupled ductile fracture criterion motivated by micromechanisms: Modeling and experiments

Ductile fracture behavior of metallic materials is significantly influenced by the stress states, especially for geometrically complex structures fabricated by laser additive manufacturing (AM) technique. This study proposes a new uncoupled ductile fracture criterion (DFC) that considers void evolution behaviors to predict the ductile fracture of AMed Ti-6Al-4V alloy. The new criterion is derived by synthetically taking into account the effects of stress triaxiality and the Lode parameter on microscopic void evolution behaviors, including void nucleation, growth, and coalescence, which eventually leads to the macroscopic ductile fracture. By comparison with the representative uncoupled ductile fracture criteria, the predictive ability of the proposed criterion for different metallic material is comprehensively discussed through a series of fracture experimental data published in the literature to verify the effectiveness and accuracy of the new criterion. The comparative studies indicate that the new uncoupled ductile fracture criterion can accurately predict fracture strain under different stress states. Particularly, the proposed micromechanism-motivated criterion demonstrates the distinguished effectiveness in predicting ductile fracture under high stress triaxiality compared to other criteria. Furthermore, fracture experiments of additively manufactured titanium alloy were conducted under various stress states to calibrate the material parameters of the proposed criterion. It can be found that the predicted fracture locus of AMed titanium alloy is more dependent on stress state and is generally lower than that of cast titanium alloy produced by traditional processing technology.

A data-driven ductile fracture criterion for high-speed impact

Data-driven methods based on machine learning (ML) models offer new approaches for characterizing the fracture behavior of advanced elastoplastic materials. In this paper, a ML-based data-driven ductile fracture criterion is proposed to characterize the fracture behavior of elastoplastic materials under high-speed impact loading conditions. To reduce the required training dataset and enhance the predictability capability, several assumptions are used. Firstly, utilizing the decoupled assumption, two separate artificial neural network (ANN) models are employed to establish the fundamental fracture model and characterize the strain rate effect of ductile fracture behavior, respectively. In addition, the enhanced method with a logarithmic function is introduced to improve predictability capability of the proposed data-driven criterion under unknown high strain rates. To establish a complete numerical implementation framework, an enhanced rate-dependent data-driven constitutive model and a compatible numerical implementation algorithm are additionally introduced. Eventually, to assess the applicability of the proposed data-driven fracture criterion, numerical simulations of notched specimens and ballistic impact conditions of Ti-6Al-4V material are conducted, respectively. These investigation results demonstrate the effectiveness of the proposed data-driven ductile fracture criterion.

The cruciality of particle size and shape on fracture mechanism of aluminum matrix composites

Metal matrix composites are generally believed to achieve better performance with spherical reinforcements than irregular ones. In this work, through experiments and computational simulations, we have demonstrated that spherical reinforcements do not necessarily enhance the tensile ductility of composites. There exists a critical size for spherical particles. Using an Al2O3-Al2024 composite as an example, we found that when the size of spherical Al2O3 particles is less than 3 µm, they are not fractured during deformation, resulting in enhanced ductility. We elucidated the competitive mechanism between particle and matrix fracture under various reinforcement sizes and volume fractions, and constructed a deformation map that can be utilized to determine fracture mechanisms. This work clarifies the micro-mechanical mechanisms of reinforcements on material fracture behavior, providing guidance for the design and fabrication of strong and ductile metal matrix composites.

Effect of random variation in input parameter on cracked orthotropic plate using extended isogeometric analysis (XIGA) under thermomechanical loading

Abstract This research introduces the Stochastic Extended Isogeometric Analysis (XIGA) method to investigate fracture behavior of isotropic and orthotropic materials under mechanical, thermal, and thermomechanical loads. Employing knot spans from Isogeometric Analysis (IGA) for domain discretization, the study utilizes identical basis functions for geometry construction and solution discretization. Utilizing Extended Finite Element Method (XFEM) enrichment functions, accurate crack face displacement discontinuity and tip singularity within the stress field are characterized. Additionally, employing a second-order perturbation technique within XIGA framework, the research derives mean and coefficient of variance values for mixed-mode Stress Intensity Factors (SIF). Stochastic variations in material elastic properties, crack length, and crack angle are considered in this computation. Credibility and robustness of the study are confirmed through comparative analyses against available literatures and Monte Carlo Simulations (MCS). The observed exceptional agreement validates the precision and reliability of the proposed stochastic XIGA method for fracture analysis in orthotropic material systems under thermomechanical loading conditions.

Identification of hardening and fracture behaviors of titanium alloy by a hybrid digital image correlation and finite element method

The reliable identification of deformation and fracture behaviors of titanium alloys is essential for accurate numerical simulation in sheet metal forming, cutting process and crash. In this study, an inverse method is proposed to identify both strain hardening and fracture behavior of titanium alloys by a hybrid experimental-finite element analysis. Uniaxial and notched tensile specimens are tested on the additively manufactured and cold rolled sheet Ti6Al4V alloys. The distributions of displacement and strain on the specimen surface during the loading are measured by digital image correlation method. An identification strategy, considering the stress–strain curve, surface strain evolution and variation of specimen width, is proposed to identify the strain hardening model parameters at large strain range. Finite element simulations are performed to update the model parameters by using the iterative inverse method. The parameters of fracture model are determined through experiments on tensile specimens in combination with numerical simulation. The experimental and simulation results show the feasibility and effectiveness of the proposed identification method, that it can be further used to characterize the plastic and fracture behaviors of other metallic materials in practice.

Accurate prediction of discontinuous crack paths in random porous media via a generative deep learning model

Pore structures provide extra freedoms for the design of porous media, leading to desirable properties, such as high catalytic rate, energy storage efficiency, and specific strength. This unfortunately makes the porous media susceptible to failure. Deep understanding of the failure mechanism in microstructures is a key to customizing high-performance crack-resistant porous media. However, solving the fracture problem of the porous materials is computationally intractable due to the highly complicated configurations of microstructures. To bridge the structural configurations and fracture responses of random porous media, a unique generative deep learning model is developed. A two-step strategy is proposed to deconstruct the fracture process, which sequentially corresponds to elastic deformation and crack propagation. The geometry of microstructure is translated into a scalar of elastic field as an intermediate variable, and then, the crack path is predicted. The neural network precisely characterizes the strong interactions among pore structures, the multiscale behaviors of fracture, and the discontinuous essence of crack propagation. Crack paths in random porous media are accurately predicted by simply inputting the images of targets, without inputting any additional input physical information. The prediction model enjoys an outstanding performance with a prediction accuracy of 90.25% and possesses a robust generalization capability. The accuracy of the present model is a record so far, and the prediction is accomplished within a second. This study opens an avenue to high-throughput evaluation of the fracture behaviors of heterogeneous materials with complex geometries.

A strain-based criterion for predicting size-dependent fracture resistance of quasi-brittle materials under mixed mode loading

In the present study, a strain-based approach called the modified maximum tangential strain criterion has been developed for evaluating size effect on the mixed-mode fracture resistance of quasi-brittle materials. This approach relies on the generalized maximum tangential strain criterion, which considers the singular (K) and the first non-singular (T) terms of Williams series expansion. Furthermore, as an important and size-dependent parameter in the proposed criterion, a new formulation is presented to calculate the critical distance (rc). The predictions of the new criterion are compared not only with the available experimental data, but also with the results estimated by another size effect criterion named the modified maximum tangential stress criterion. It is shown that the proposed strain-based criterion is highly capable of estimating the size-dependent mixed-mode fracture behavior of quasi-brittle materials without requiring to compute the other higher order terms.

{10-12} twinning transfer behavior in compressed high-purity hafnium

The interaction between twins and grain boundaries (GBs) significantly influences material deformation and fracture behavior. In the present study, high-purity hafnium (Hf) was subjected to compression at both room temperature and under liquid nitrogen cooling conditions. Twinning transfer (TT) behavior of {10–12} <−1011> extension twin was thoroughly and statistically investigated. Results show that compression temperature affects the misorientation angle (MA) for TT. Under room temperature compression, twins can transfer across GBs with MAs below 30° and partially transfer across GBs with MAs between 30° and 50°. When compressed under liquid nitrogen cooling, twins can traverse the GBs with MAs below 40° and partially traverse the GBs with MAs above 40° and with a maximum MA of 77°. The MA, Schmidt factor (SF) value, and geometrical compatibility parameter m’ of twinning systems in neighboring grains influence the TT. Favorable conditions for TT include low MAs, high SF and m’ values. Stress concentration caused by incoming twins can be alleviated through TT with high m’ at GBs with low MAs. For GBs with high MAs, stress concentration can also be alleviated through TT or twinning-slipping transfer with high m’. Extension and growth of outgoing twins contribute to further stress concentration relief.

Effect of Bi content and temperature on the shear mechanical properties of Fe-Bi nanocomposites: a molecular dynamics study

In this study, the effects of Bi content and temperature on the mechanical properties of Fe–Bi nanocomposites were investigated using molecular dynamics simulation. The research reveals that the nanocomposite’s shear strength reaches a peak of 3.785 GPa at a Bi content of 0.15%, attributed to the impediment of dislocation movement by twin boundaries during shearing, resulting in a dynamic ‘Hall–Petch’ effect and exceptional shear performance of the material. The abundant twinning induced around Bi phase inclusions introduces orientational disparities within the crystal, leading to grain misalignments, with dislocations in the grains slipping near the twin boundaries. In the nanocomposites, <100> dislocations merely act as initial sites for reactions, reducing their impact on the material’s strength and fracture behavior. The maximum stress decreases with increasing temperature while the magnitude of atomic transformations increases. The proportion of atoms at grain boundaries is higher at higher temperatures, and the arrangement of atoms at grain boundaries is more complex. At a temperature of 100 K, the dislocation density is highest with the smallest variation, forming a reinforced region within the material. The above results have significant implications for the design of environmentally friendly Bi-containing free-cutting steels.

Modelling the effects of void swelling and spatial heterogeneity on the fracture of metallic materials by crystal plasticity

To theoretically analyse how void swelling and spatial heterogeneity impact the fracture behaviour of metallic materials, a coupled porous crystal plasticity framework has been developed. The proposed framework is then applied to analyse the fracture behaviour of metallic materials under different swelling conditions and types of spatial heterogeneity. It is revealed that at low porosity, the spatial heterogeneity of voids will have limited influence on the fracture behaviour of the material. However, at high porosity, owing to void swelling, a concentrated distribution of voids near grain boundaries can lead to a strong deformation localization, which can be seen as an indicator of possible quasi-brittle fracture. It is further discovered that the inner pressure of the voids tends to reduce the yield stress of the material and promote localized plastic deformation. As a result, such pressure will enhance the impact of concentrated distribution of voids, which can lead to further embrittlement of the material. The present study reveals the key role of void swelling and spatial heterogeneity in regulating the fracture behaviour of metallic materials, a step towards a better understanding over the failure mechanisms of metallic materials under extreme conditions.

Modeling of the fracture behaviors of concrete using 3D discrete element method with softening effect

Understanding the fracture mechanism of concrete is very important for the safety design of concrete structures. We develop a 3D discrete element model with softening effect to study the fracture behaviors of quasi-brittle materials. The basic ideas of our model inspired from the flat-joint concept and the cohesive crack model are implemented in the framework of MUSEN, which is an open source discrete element software with CPU–GPU accelerating computation. The placement-package-compaction method is proposed together with laser scanning technology to construct the meso-scale geometric model of concrete. The meso-parameters of 3D discrete element model developed are calibrated by uniaxial compression and splitting tension tests of concrete. The validation of the present model is verified by the laboratory test of concrete. Compared with the results predicted by the flat-joint model, the F-CMOD curves and fracture parameters simulated by our model are in good agreement with that of the laboratory tests of concrete. Finally, it is concluded that the fracture strain of bond significantly affects the fracture behavior but the softening mode does not. It is found that the linear one is better choice among three softening modes in the present model.

Experimental investigation on fatigue and fracture behaviour of cold recycling materials

Cold Recycled Material (CRM) has emerged as a highly innovative road construction material, offering numerous advantages over conventional Hot Mix Asphalt (HMA), such as reduced construction costs, decreased energy consumption, and enhanced resistance to reflective cracking. CRM is primarily composed of Reclaimed Asphalt (RA) and bitumen emulsion, with the addition of cement as a co-binder. However, the presence of cement in CRM can lead to increased susceptibility to cracking under heavy traffic loads. In this study, the fracture-fatigue behaviour of CRM modified with by-product fillers was investigated in order to improve the overall performance of CRM mixtures. The Cyclic Indirect Tensile Fatigue test (CIT-CY) and Semi-Circular Bending (SCB) fracture tests were conducted on the CRM mixtures and mortars, respectively. The findings reveal that CRM materials incorporating specific fillers demonstrated a balanced combination of fatigue and fracture resistance, indicating the potential for these modified CRMs to enhance road construction applications.

Discrete Element Method Simulation of Particulate Material Fracture Behavior on a Stretchable Single Filter Fiber with Additional Gas Flow

This study presents a comprehensive discrete element method (DEM) simulation approach for the stretching of a filter fiber with a separated polydisperse particle structure on top. For a realistic interaction between the fiber surface and the particles, the original surface of the polymer fiber was projected onto the surface of the fiber cylinder using surface imaging technologies (atomic force microscopy (AFM) and white-light interferometry). In addition, the adhesive forces between particle–fiber and particle–particle contacts were calibrated in the DEM domain using values from self-conducted AFM measurements. Fiber stretching was implemented by the linear motion of small periodic fiber elements. Discretization problems were resolved through studying the stretching of a fiber segment at the size of 8 mm. A critical fiber element length was discovered to be ≈100 μm for minimizing discretization dependencies during the cracking of the particle structure. The number and density of particle–particle contacts within the particle loading on the fiber were obtained at two different elongation rates. Effects such as densification of the particulate structure and increased detachment due to additional air flow were demonstrated.