Fracture Behavior Of Materials Research Articles

A unified viscoelastic model of progressive damage and failure for solid propellants

A general viscoelastic model incorporating the progressive damage evolution and failure criterion is developed for solid propellants across a wide range of temperatures (223 K to 333 K) and strain rates (2.38 × 10−4 /s to 4.76×10−2/s). (i) The progressive damage evolution, characterized by continuous void cavitation and growth, is linked to a macroscopic damage variable derived from a simple damage potential threshold, making it possible to determine the microstructural damage from experimental data. (ii) The failure criterion introduces two microstructural ingredients: the strain energy density, which accounts for both the glassy and rubbery failure of the polymer matrix, capturing brittle and ductile fracture modes at low and high temperatures respectively; and the void volume limit accounts for interface debonding, a process of particle detachment from the matrix. The implementation of the model effectively predicts the damage response and failure strains under uniaxial tension, cyclic and complex loading as well as superimposed pressure. Results reveal strong temperature/strain-rate dependency in the tensile strength, volume dilatation, and failure strains. Given that the model unifies progressive damage with ultimate failure and requires only a few model parameters, it assists in establishing a fracture criterion for the nonlinear fracture behavior of viscoelastic materials.

A machine-learning interatomic potential to understand the anisotropic fracture behavior of BaZrO3 material

The complex operating environment severely tests the mechanical stability of the electrolyte material BaZrO3 (BZO), which affects the performance of solid oxide fuel cells(SOFCs). Molecular dynamics (MD) simulation provides an efficient method to research the mechanical behavior of nanocrystalline materials. In the interest of researching the mechanical behavior of BZO materials utilizing a machine learning (ML) MD approach, this article has established the most effective ML potential with DFT reliability. By contrasting the lattice constants and elastic constants with the DFT data, the precision of the potential was confirmed. By simulating the uniaxial tensile mechanical behavior of the BZO models without crack and with a central crack in the crystal orientation of [100] and [110], we found that the BZO material has a significant anisotropic property. In the crack-free model, the BZO crack propagation mode in the [100] crystal orientation is a shear fracture. The central microcrack tilts downward and expands symmetrically in the [110] crystal-oriented BZO model. When the initial structure with a central crack, the fracture mode changes significantly, and in both crystal orientations, the crack fracture along the BaO plane, the crack expands horizontally in the BZO model in the [100] crystal orientation and the crack expands zigzag in the BZO model in the [110] crystal orientation. The calculations of fracture strength, critical energy release rate, and fracture toughness show that the [110] crystal-oriented BZO has a stronger resistance to fracture than the [100] crystal-oriented BZO model.

Phase-field modeling of stochastic fracture in heterogeneous quasi-brittle solids

Owing to the random nature of heterogeneity, damage and fracture behavior of quasi-brittle materials exhibits a considerable degree of uncertainty. Computational modeling of stochastic fracture in quasi-brittle materials has become an indispensable tool for analysis and design of engineering structures. To this end, we present in this paper a computational framework to capture probabilistic fracture in heterogeneous quasi-brittle solids by combining the random field theory and the phase-field cohesive zone model (PF-CZM). The spatial variation of the material strength and fracture energy is represented by a cross-correlated bivariate random field generated by the Karhunen–Loève expansion. The recently proposed PF-CZM is employed to simulate the stochastic crack nucleation and propagation in quasi-brittle solids. The objectivity of the Monte-Carlo simulation is achieved by imposing a specific condition on the phase-field length scale parameter and the correlation length of the random field. In particular, upon this condition the width of the fracture process zone (FPZ) is considerably smaller than the correlation length of the random field such that the material inside the FPZ does not exhibit significant spatial variations of mechanical properties. As the fracture energy is intrinsically incorporated in the PF-CZM, it is unnecessary in this case to explicitly consider the FPZ width. The resulting probabilistic PF-CZM together is applied to the Monte-Carlo simulations of fracture in concrete structures of different geometries. It is shown that the stochastic simulation results are insensitive to both the phase-field length scale parameter and the finite element mesh discretization as in the previous deterministic analyses. Enhanced with the specific condition on the involved characteristic lengths, the PF-CZM provides a viable tool for stochastic simulations of damage and fracture in quasi-brittle structures.

Microscopic R-curve simulation study of asphalt material fracture

Cracks can significantly influence the service life of an asphalt pavement. To study the microcracking behavior of asphalt materials, this paper utilized molecular dynamics simulation methods to simulate the tensile fracture process of asphalt materials at the microscopic level and described the fracture behavior using R-curve. Two experimental factors, temperature and loading rate, were selected to simulate the tensile fracture of virgin asphalt binder, aged asphalt binder, and SBS modified asphalt binder, and Microeconomic R-curve were constructed based on the fracture displacement and cumulative fracture energy of asphalt materials. Meanwhile, fracture energy, cohesive energy, and energy rate were used to evaluate the fracture behavior of asphalt materials. The results indicated that the micro-R curve simulated by molecular dynamics can well describe the tensile fracture behavior of asphalt. Among the fracture indicators, fracture energy and energy rate were significantly affected by the type of asphalt, while cohesive energy was significantly affected by the loading rate.

In-situ EBSD observation and simulation of free surface roughening and ductile failure in the ultra-thin ferritic stainless steel sheet

Surface roughening is one of the most fundamental issues which greatly affects the plastic deformation and ductile fracture behavior of ultra-thin sheet materials. The present study investigated the influence of free surface roughening on the micromechanical failure in the ultra-thin ferritic stainless steel (FSS) sheet for bipolar plate in proton exchange membrane (PEM) fuel cell under in-situ tensile deformation. The microstructural evolution during uniaxial tension was monitored using in-situ electron backscatter diffraction (EBSD) technique. Then the initial microstructure was directly mapped onto the finite element mesh of representative volume element (RVE) in the crystal plasticity finite element (CPFE) simulation. The CPFE model was incorporated with the microscopic ductile fracture criterion in terms of plastic energy dissipation in order to simulate the initiation of ductile fracture caused by the free surface roughening. The in-situ EBSD observations reveal that the microstructure of the ultra-thin FSS sheet exhibits heterogeneous plastic deformation and strain localization on the surface at the large deformation owing to the considerable free surface roughening. The CPFE simulations well reproduce the stress/strain heterogeneity and the local hotspots of the ductile fracture initiation. It reveals that the increase of surface roughness with the deformation results in the increased inhomogeneity of thickness which accelerates the strain localization, consequently the premature necking and failure in the ultra-thin steel sheet. Due to the free surface roughening which can facilitate strain localization, the initiation of ductile fracture is obviously observed in both the ridges and valleys in the free surface and its propagation along the pronounced localization band through the thickness, leading to material failure. The good correlation of free surface roughening to the onset of plastic instability and ductile fracture further advances the insight into the micromechanical failure during plastic deformation of the ultra-thin FSS sheet for bipolar plate in PEM fuel cell.

Effect of crack angle and concrete strength on the dynamic fracture behavior of rock-based layered material containing a pre-existing crack

Effect of crack angle and concrete strength on the dynamic fracture behavior of rock-based layered material containing a pre-existing crack

Phase field model for brittle fracture in multiferroic materials

Multiferroic materials, which simultaneously possess piezomagnetic, piezoelectric, and electromagnetic coupling effects, have a wide range of applications in various fields. Multiferroic materials are generally brittle with low fracture toughness, and accurate prediction of the fracture behaviors of multiferroics is challenging. In this work, a phase field model for brittle fracture in multiferroic materials is developed with the help of the Hamilton principle. In light of the second law of thermodynamics, the constitutive equations are derived in the context of the phase field method. The present theoretical framework unifies two classical phase field models and four combinations of the electric and magnetic boundary conditions. The residual controlled staggered algorithm, which enjoys a higher accuracy and lower computational cost, is extended to the fracture problems in the context of magneto-electro-elasticity. Systematic numerical simulations are performed in both 2D and 3D cases. The influences of the external magnetic field, electric field, and electric and magnetic boundary conditions on fracture behaviors of multiferroic materials are studied in detail. The applied magnetic field may not only accelerate or delay the fracture, but also influence the crack path. The present work is beneficial to assess the safety of multiferroic-based devices in engineering applications.

The influenced zones of stress intensity factor and plasticity at multi-crack tips

The influence range of crack interaction is studied using the distribution dislocation technique, and is defined as the influenced zone. For elastic materials with cracks, the equivalent stress intensity factor influenced zone is obtained, while for plastic materials with cracks, the plasticity influenced zone is determined. The interaction between multiple cracks can be analyzed by introducing the concept of the influenced zone, which simplifies the analysis. The results indicate that if a crack is located outside the influenced zone of another crack, the effect of the former on the latter can be ignored within an acceptable range of error. The influenced zone for elastic materials depends on the length and inclined angle of a crack, whereas for plastic materials, the plastic influenced zone is affected by the crack length, inclined angle, and material yield limit simultaneously. In the case of plastic materials with multiple cracks, fusion of plastic zones between two cracks may occur at certain positions under the influence of other cracks. These theoretical findings can simplify the analysis of the fatigue fracture behavior of materials with multiple cracks, whether they are elastic or plastic.

From macro fracture energy to micro bond breaking mechanisms – Shorter is tougher

We show a novel fracture behavior and properties of brittle materials not previously explored. These were made possible when merging macro to micro in fracture. Our findings are based on macro-scale fracture cleavage experiments of dynamic cracks propagating in brittle single-crystal silicon specimens, focusing on the crack’s energy-speed relationships, and the fine details of the crack front. From the micro-scale, we developed an atomistic model for bond-breaking mechanisms. These mechanisms are in the form of low-energy kink advance (migration) and high-energy kink formation (nucleation) along the crack front. The energy release rate (ERR) at crack initiation, G0, and its derivative, dG0/da≡Θ, in particular, play a major role in the novel behavior and properties. G0 and Θ are influenced by the precrack length, a0. The macro-scale experiments, the micro-scale atomistic model, and the gradient of the ERR, Θ, enabled the conclusions portrayed in this work.We identified that the cleavage energy is not a constant but bounded by the Griffith Barrier as the lower bound while the upper bound (apparently the lattice-trapping barrier) may reach 3 times the lower bound. We further suggest that a brittle material can be envisaged as comprising a pseudo-R-Curve behavior mechanism typical of metallic materials. A new and essential fracture mechanism was identified, which we term ‘quasi-propagation’, a transitional mechanism between initiation and propagation. During this mechanism, the sequence of the bond-breaking mechanisms is varying, causing an increase in the macroscale cleavage energy.The evaluated cleavage energy shows another novel behavior, that of ‘shorter is tougher’, namely, shorter cracks require higher energy to propagate, and, therefore, specimens with shorter cracks are stronger than that predicted by Griffith’s theory.

Effect of broaching pre-cracking process on fracture behavior of polymeric materials

Effect of broaching pre-cracking process on fracture behavior of polymeric materials

Statistical analysis of slip transfer in Al alloy based on in-situ tensile test and high-throughput computing method

Slip transfer mechanism is studied based on in-situ tensile tests performed on an Al-Mg alloy and high-throughput computing. A statistical analysis of slip transfer is performed for over 1180 grain boundaries and 155,250 slip pairs while considering the local lattice rotation, grain boundaries, and slip system geometries. Two new slip transfer parameters, N and B, representing the alignment of the slip planes and the activation of slip systems in adjacent grains, are proposed. A decision tree model is built to evaluate the prediction accuracy of the slip transfer parameters. The optimized results of the decision tree classifiers show that the two new parameters are more effective than the Luster–Morris parameter, m′. The improvement in the classification accuracy is attributable to the information regarding the slip plane geometry and orientation evolution contained in N and B. The new slip transfer parameters improve our understanding of the slip transfer mechanism and can be integrated into plasticity models to predict the deformation and fracture behaviors of polycrystalline materials.

Numerical study and experimental validation of the size effect of smooth and mode I cracked semi-circular bend specimens

The edge-cracked semi-circular bend (SCB) specimen subjected to three-point bending loading is used in many applications to measure the fracture behavior of quasi-brittle materials. The main objective of the present work was to study the effect of the crack length to SCB specimen radius ratio (a/R), span to specimen diameter ratio (S/D), and specimen size on its flexural and mode I crack growth behavior. The contour integral method was implemented using the 3-D finite element method to determine the mode I stress intensity factor. In addition, high-strength concrete specimens were experimentally studied to validate the numerical results. The results show that the maximum compression stress is not sensitive to the S/D value, while the tensile stress is very sensitive. The value of S/D is the main parameter controlling the crack driving force (i.e., the crack mouth opening displacement (CMOD) and the normalized stress intensity factor, YI). For the same S/D, the SCB specimen diameter value change has a marginal effect on CMOD and YI. The specimen with S/D = 0.8 showed that it is the most compatible specimen with three-point bending test conditions, regardless of the SCB specimen size. A good agreement between the numerical and experimental results was achieved.

A modified MERR model for predicting mode II fracture initiation angle considering boundary constraint effect

AbstractDuring the service process of brittle materials like marble, soda‐glass, and acrylic, mode II fracture is usually a typical failure mode. The fracture crack initiation, which is a critical factor affecting mode II fracture behavior, is an essential issue for understanding the fracture mechanism and determining fracture toughness. This paper proposed a modified maximum energy release rate model to predict the mode II fracture initiation angle through superimposing two idealized boundary conditions, remote loading, and crack‐face traction. The degree of the boundary constraint effect in finite‐size specimens was quantified by introducing the dimension‐ratio parameter. As experimentally validating through tension‐loading shear fracture tests of brittle poly(methyl methacrylate) (PMMA), the proposed model was demonstrated to be a good prediction of the mode II fracture initiation angle. The applicability of the proposed model was also verified with other brittle materials and fracture test techniques in references. The findings provide an insightful understanding of the mode II fracture behavior of brittle materials.

Simulation and research on fracture behavior of vehicle structural alloy materials based on XFEM

Aluminum alloy 7050 has been widely used in the structure of aerospace vehicles because of its excellent comprehensive performance. In this paper, based on the extended finite element method and classical theory, the material parameters in the finite element simulation are calculated, next the metal plate with a central pre-crack is analyzed for static load breaking and fatigue damage under cyclic loading, the observation of different loading levels and the damage characteristics under different preset crack lengths are summarized, the rules are summarized to provide support for follow-up work.

Size effect on fracture behavior of quasi-brittle materials during uniaxial compression tests

Size effect on fracture behavior of quasi-brittle materials during uniaxial compression tests

Determining the fracture toughness of quasi-brittle materials with notched four-point bending tests

Fracture is common failure mode of quasi-brittle materials when suffering tensile loads, the accurate determination of the fracture toughness becomes extremely vital. Notched four-point bending (4-p-b) test is one of main fracture test methods, but is rarely applied in evaluating the fracture behavior of quasi-brittle materials. In this study, on the basis of relevant standards, the specific requirement of 4-p-b fracture test is proposed. Then the closed-form solution is used to establish the relation between the four-point bending test results and fracture toughness on the basis of the Boundary Effect Model. The influence of test conditions, boundary effect and distribution characteristics of fracture properties are discussed in detail. After that, two types of hard rock and concrete are utilized to verify the reliability of proposed methods. The results show that four-point bending test and corresponding analytical solution are suitable for determining the fracture toughness of quasi-brittle materials, regardless of the different initial notch length and material categories.

An extended peridynamic model for analyzing interfacial failure of composite materials with non-uniform discretization

This work presents an extended ordinary state-based peridynamic model and approaches to analyze the fracture behavior of composite materials considering interfacial failure. An interface force term is introduced to characterize the interaction among different compositions in composite materials, which enables naturally the non-uniform discretization to be conveniently adopted, especially where sharp interfaces exist. The calculation of force states in different compositions is independent of each other, and the use of non-uniform discretization can improve computational efficiency significantly. Further, inspired by the cohesive zone model (CZM), the deformation coefficient and degradation behavior of interface bonds are derived by using the traction-separation law, and a mixed-mode fracture criterion for interface bonds based on the bond energy density is established as well. Validation of the proposed model and approach is established through a classical rectangular plate example, and then the proposed model is employed to analyze the failure of typical composites including laminated glass and concrete. The results show good agreement with corresponding experimental observations and it indicates that the proposed extended peridynamic model can accurately and efficiently capture and describe the fracture of composite materials with sharp interfaces.

3-D coupled peridynamics and discrete element method for fracture and post-fracture behavior of soil-like materials

The present paper investigates a 3-D numerical analysis method, combining peridynamics (PD) and the discrete element method (DEM), which can simultaneously handle both the fracture and post-fracture behavior of materials assumed to be soils. With geomaterials, it is very important to treat the process from fracture to post-fracture in a continuous manner. The bond-based PD model is employed to reproduce the behavior from the initiation of cracks to fracturing. At the same time, the DEM model is also introduced so that the contact forces among the fragmented pieces can be calculated after the fracturing. The computational process of the physical contact between the wall element and the computational nodes of the PD is also solved based on the DEM so that plane geometry boundaries can be used. For the failure criteria of the connection between the computational nodes of the PD, a bilinear type of bond model is introduced to obtain a nonlinear stress–strain relationship and numerical stability when the calculation process switches from PD to the DEM. To verify the proposed approach, numerical simulations of the diametral compression test are performed on flawless cylindrical specimens, and the results are compared with theoretical solutions for the stress distribution inside the specimens. Based on the results, a simulation of the compressive failure of multiple soil-like crushable objects is performed as an example of the application of the coupled PD-DEM. The obtained results show that the proposed method will serve as a computational framework that can treat the continuous fracture behavior of soil-like materials in three dimensions.

Thermal effects on fracture and the brittle-to-ductile transition.

The fracture behavior of brittle and ductile materials can be strongly influenced by thermal fluctuations, especially in micro- and nanodevices as well as in rubberlike and biological materials. However, temperature effects, in particular on the brittle-to-ductile transition, still require a deeper theoretical investigation. As a step in this direction we propose a theory, based on equilibrium statistical mechanics, able to describe the temperature-dependent brittle fracture and brittle-to-ductile transition in prototypical discrete systems consisting in a lattice with breakable elements. Concerning the brittle behavior, we obtain closed form expressions for the temperature-dependent fracture stress and strain, representing a generalized Griffith criterion, ultimately describing the fracture as a genuine phase transition. With regard to the brittle-to-ductile transition, we obtain a complex critical scenario characterized by a threshold temperature between the two fracture regimes (brittle and ductile), an upper and a lower yield strength, and a critical temperature corresponding to the complete breakdown. To show the effectiveness of the proposed models in describing thermal fracture behaviors at small scales, we successfully compare our theoretical results with molecular dynamics simulations of Si and GaN nanowires.

Study on fracture behavior of PMMA materials under the action of shaped charge with different diameters

Study on fracture behavior of PMMA materials under the action of shaped charge with different diameters