Fracture Energy Dissipation Research Articles

Discrete softening-damage model for fracture process representation with embedded strong discontinuities

A damage softening model is implemented into a discrete lattice framework with embedded strong discontinuities for the discontinuous representation of fracture. Such a model fits heterogeneous framework and allows capturing the complex fracture mechanisms in quasi-brittle materials under various quasi-static and dynamic loading conditions. Finite element implementation of damage softening constitutive model provides a very powerful computational tool for a description of material degradation processes which happen during monotonic loading, as well as unloading and reloading on the damaged material. In particular, the proposed model can capture the processes such as reduction of material stiffness, crack opening-closing mechanisms and reloading that follows the inverse of compliance modulus. Numerical examples are performed to demonstrate the effectiveness and robustness of the model fracture capabilities. The two examples deal with quasi-static fracture mechanisms of a heterogeneous material. The fragmentation of a cylinder in dynamics framework subjected to internal pressure and inertial forces is given as well. The plots of all components of internal energy (the dissipated fracture energy, elastic strain and kinetic energy) in dynamic fracture process are provided. The model of this kind can simulate multiple cracks formation, coalescence, propagation and mesh independent results.

Improved Fracture Toughness and Conversion Degree of Resin-Based Dental Composites after Modification with Liquid Rubber.

There are many methods widely applied in the engineering of biomaterials to improve the mechanical properties of the dental composites. The aim of this study was to assess the effect of modification of dental composites with liquid rubber on their mechanical properties, degree of conversion, viscosity, and cytotoxicity. Both flow and packable composite consisted of a mixture of Bis-GMA, TEGDMA, UDMA, and EBADMA resins reinforced with 60 and 78 wt.% ceramic filler, respectively. It was demonstrated that liquid rubber addition significantly increased the fracture toughness by 9% for flow type and 8% for condensable composite. The influence of liquid rubber on flexural strength was not statistically significant. The addition of the toughening agent significantly reduced Young’s modulus by 7% and 9%, respectively, while increasing deformation at breakage. Scanning electron microscopy (SEM) observations allowed to determine the mechanisms of toughening the composites reinforced with ceramic particles. These mechanisms included bridging the crack edges, blocking the crack tip by particles and dissipation of fracture energy by deflection of the cracks on larger particles. The degree of conversion increased after modification, mainly due to a decrease in the matrix resin viscosity. It was also shown that all dental materials were nontoxic according to ISO 10993-5, indicating that modified materials have great potential for commercialization and clinical applications.

Fracture behavior and damage mechanisms of sandstone subjected to wetting-drying cycles

Rocks are usually subjected to cyclic wetting-drying due to the periodical changes in moist condition. To investigate the effect of wetting-drying cycles on the fracture behavior of sandstone, notched semi-circular bending tests were performed on sandstone samples after every ten cycles (a total of 50 cycles) under both quasi-static and dynamic loading conditions. Tests results indicate that both of fracture toughness and energy dissipation of sandstone significantly decrease with the increase of cycle number. Moreover, the microstructural characteristics reveal that after cyclic wetting-drying treatments, the calcite cementation between grains gradually dissolves and the density and width of inter-granular fracture increase, which could be responsible for the deterioration of rock mechanical properties.

Simultaneously enhancing strength and toughness of Zr-based bulk metallic glasses via minor Hf addition

Zr65.5-xHfxNb3Cu13Ni11Al7.5 (x = 0.0, 0.5, 1.0, 1.5 and 2.0 at.%) bulk metallic glasses (BMGs) were successfully prepared by copper mold casting. The effects of minor Hf addition on the mechanical properties and fracture mechanisms were investigated. The quasi-static compressive mechanical properties of Zr65.5-xHfxNb3Cu13Ni11Al7.5 alloys were significantly improved by Hf addition. The optimum compressive fracture strength (σf) and fracture strain (εf) are 1516 MPa and 2.6%, respectively, for the Zr64.5Hf1.0Nb3Cu13Ni11Al7.5 alloy. The impact toughness of the Zr64Hf1.5Nb3Cu13Ni11Al7.5 alloy (Ak = 127 kJ/m2) is nearly four times than that of the Zr65.5Nb3Cu13Ni11Al7.5 alloy (Ak = 33 kJ/m2). The increase of the fracture surface area and the ratio of vein-like patterns regions caused by Hf addition play an important role in fracture energy dissipation under dynamic loading. The dependence of mechanical properties on the Hf content is closely related to the variation of free volume in the current alloys. The relationship between the Hf addition and the free volume change is discussed in detail. These results may provide new insights into simultaneously enhancing the plasticity and toughness of BMGs with minor alloying.

Strain localization in reduced-order asymptotic homogenization

A reduced-order asymptotic homogenization-based multiscale technique that can capture damage and inelastic effects in composite materials is proposed. This technique is based on a two-scale homogenization procedure where eigenstrain representation accounts for the inelastic response and the computational efforts are alleviated by a reduction-of-order technique. Macroscale stress is derived by calculating the influence tensors from analysis of a representative volume element. At microscale, the damage in the material is modeled using a framework based on continuum damage mechanics. To solve the problem of strain localization, a method of alteration of the stress–strain relation of microconstituents based on the dissipated fracture energy in a crack band is implemented. The issue of spurious postfailure artificial stiffness at macroscale is discussed and the effect of increasing the order to alleviate this problem is checked. Verification studies demonstrated that the proposed formulation predicts the macroscale response and also captures the damage- and plasticity-induced inelastic strains.

Spark plasma-sintered MoSi2-reinforced Y−α−SiAlON ceramics: mechanical and high temperature tribological properties

Silicon aluminum oxy-nitride commonly abbreviated as SiAlON is indeed one of the most promising non-oxide engineering ceramics due to its ease of formation compared to extremely covalent silicon nitride ceramic and scope of tailoring the material properties as per application demand. To make it more suitable for high-performance applications, composites containing various secondary phases have been attempted so far to improve the mechanical performance over its monolithic counterpart. In the present work, reinforcement of particulate molybdenum disilicide (MoSi2) in Y-α-SiAlON matrix has been undertaken under spark plasma sintering (1750 °C, 10 min, 50 MPa die pressure) followed by Vickers hardness (HV), fracture toughness (KIC), and high-temperature tribological properties under different conditions of the formed composites containing 10 and 20 wt.% secondary phase were investigated. Sintered specimens were ≥ 97.5% dense with negligible porosity. Addition of MoSi2 in Y−α−SiAlON resulted in reduced HV. The 20 wt.% MoSi2/Y−α−SiAlON composite showed ~ 11% lower HV1 compared to the monolith. On the contrary, KIC of the 20 wt.% MoSi2/Y−α−SiAlON composite was found to be around 24% higher compared to pure Y−α−SiAlON (KIC ≈ 3.9 MPa-m0.5). Additional fracture energy dissipation through crack deflection and bridging by the dispersed MoSi2 particulates was the primary reason behind obtaining higher fracture toughness for the composites. Unlubricated reciprocating ball-on-disc experiments against dense silicon nitride ball revealed a significant effect of MoSi2 oxidation in achieving improved wear resistance of the composites over the monolith, especially, beyond 300 °C in ambient air under applied normal loads up to 90 N and sliding distance up to 70 m.

Fracture Behaviour of Recycled Aggregate Concrete Beams – An Experimental Study

The purpose of this research is to assess the effect of recycled aggregates on the fracture energy properties of concrete under various notch depths. In this studyfracture energy of recycled aggregate concrete beams of size 700mmx150mmx150mm with notches of size 7.5mm, 15mm, 45mm and 75mm were provided to study the fracture energy properties like unstable fracture toughness and Crack Mouth Opening Displacement (CMOD). A clip gauge of + 4mm range over a gauge length of 25mm was fixed across the notch at the bottom face of the beam to measure the crack mouth opening displacement (CMOD). Linear varying differential transformer (LVDT) of two numbers was used to determine the deflection of the specimens. Specimens of two water/cement ratios 0.5 and 0.45 were adopted to study the fracture energy and the results were compared. Fracture parameters such as unstable fracture toughness were predicted using empirical relations. Fracture studies elucidates that fracture energy dissipation increases with increase in the notch depth. Also fracture energy dissipation and CMOD of recycled aggregate concrete is more compared to conventional aggregate concrete due to the higher water absorption capacity of recycled aggregates.

Block coordinate descent energy minimization for dynamic cohesive fracture

A block coordinate descent algorithm within a discontinuous Galerkin finite element formulation is proposed for both explicit and implicit energy minimization in solid bodies in which rigid-cohesive fractures initiate and propagate. The crack opening dependent Barenblatt type surface cohesive energy function is non-differentiable at the origin. In each iteration or each explicit update, the algorithm minimizes the potential with respect to each crack opening displacement unknown and with respect to the block of deformation unknowns, sequentially. This decomposes minimization of the full non-differentiable problem into a number of “small” non-differentiable sub-problems that must be solved locally at the inter-element boundaries of the finite element mesh and an “easy” differentiable sub-problem that characterizes global equilibrium. As a result, non-differentiability is effectively treated locally and the algorithm can be easily incorporated into standard finite element codes. On the basis of a convexity analysis of the proposed non-differentiable energy functional, we obtain a minimum cohesive process zone resolution criterion, known empirically in the previous literature as a requirement for capturing the amount of dissipated fracture energy correctly. The method is free of any regularization parameters and preserves the discrete nature of fracture without introducing a stress discontinuity at initiation of decohesion. Robustness of the method is shown through several numerical examples of fragmentation and branching and through comparisons with existing numerical and experimental results.

Microstructure and mechanical properties of sandwich copper/steel composites produced by explosive welding

The explosive welding process is widely used for fabrication of layered composites. However, many problems connected with microstructure formation near the interface during explosive loading and the dependence of composites final properties from fabrication technique and subsequent treatment are unclear. In the present work, we researched feature of interface structure, microstructure and mechanical properties of sandwich composites on base of copper and low carbon steel joined by the explosive welding. Three-layered copper/steel/copper composites have wavy interfaces which were caused by the effect of plates impact collision. Cold rolling was used as additional hardening process of a welded sandwich composites. It was found that wavy interface after cold rolling acquires a waveless profile. According to EBSD analysis, explosive welding and cold rolling with a total reduction of 50% resulted in grain refinement in copper and steel layers due to the development of dynamic polygonization and recrystallization processes. From the results of tensile tests, it was determined that the sandwich composites have higher strength properties as compared to initial copper in 1.8–3.5 times. The high values of impact strength of sandwich composites are attributed to the influence on ductile copper layers and fracture energy dissipation at the expense of crack deviation while crossing the interfaces.

Influence of polymer electrospun nanofibers on thermal properties of epoxy resins

Electrospinning of polymers has gained surging interest in the last decades due to its wide range of applications in different fields, such as sensors, electronic devices, separation systems, biomedical materials. Still there are only few reports on the use of these nanofibers as reinforcement in polymer composites. In this paper, solution electrospinning was employed to produce nanofibrous mats impregnating two epoxy resins to form “monolayer“ systems, with the aim to study the influence of the nanofibers on both the curing behaviour and the morphology of the resin systems. Three polymers were chosen for producing electrospun mats, a polysulfone (PSF), a polyamide Nylon 6,6 (Ny66) and a polyacrilonitrile (PAN). The nanofibrous mats were employed to produce mat/epoxy monolayers by soaking the mat in two different epoxy resin systems, one in lab-synthesized-high performance, and the other commercial-low performance.The results show a different extent of swelling of the electronspun mats, as derived by morphological analysis. The observation of the fractured surfaces also indicates the formation of several fracture planes or phase separation phenomena, suggesting the possibility of dissipation of fracture energy by the epoxy/mat nanocomposites. Additionally, for all resin/mat arrangements, thermal analysis indicates no significant interference of the mat with the cure reactions of the resins and only slight changes of the glass transition temperatures.

The effect of nanoalumina silanisation in tetraglycidylether epoxy adhesive

The efficiency of different surface modifications on alumina nanoparticles on both filler dispersion and the final properties of the resulting adhesive nanocomposites have been investigated. A tetraglycidyldiaminodiphenylmethane (TGDDM) epoxy resin and three sample series of nanocomposites were prepared via in-situ incorporation of alumina nanoparticles into the reactor. The alumina/TGDDM nanocomposites were prepared individually using neat or non-treated alumina nanoparticles and two kinds of silane-grafted alumina nanoparticles, i.e., APS-treated alumina and GPS-treated alumina. The presence of different alumina nanoparticles in the epoxy matrices resulted in different states of nanofiller dispersion as revealed in SEM and AFM micrographs. It was elucidated that the silane treatment on alumina nanoparticles is crucial for the desired dispersion in the epoxy matrix. Besides, the appropriate filler dispersion resulted in improved thermal resistance and high degree of cure, especially for the adhesive nanocomposite containing APS-treated alumina nanoparticles. In adhesion tests, the shear strength was improved in both nanocomposites containing silane-grafted alumina with more pronounced values for the nanocomposite containing APS-treated alumina nanoparticles. The shear strength reached from 6.6 MPa for the neat epoxy adhesive to 10.2 MPa for the adhesive nanocomposite containing 5 wt % APS-treated alumina nanoparticles mainly due to high levels of dispersion of the high modulus alumina nanoparticles and effective interfacial interactions with the epoxy matrix. The adhesive peel strength of alumina/TGDDM nanocomposites showed a similar trend as in shear strength with more pronounced variations. A noticeable increase in the peel strength of the nanocomposites containing silane-grafted alumina nanoparticles appeared to correlate with greater levels of crack deflection and hence dissipation of fracture energy as observed in SEM pictures.

Three-dimensional mesoscopic simulation of the dynamic tensile fracture of concrete

Despite its ubiquitous presence in the built environment, the dynamic tensile fracture behaviour of concrete under a high strain rate is still not completely understood. In this study, a three-dimensional meso-scale finite element model is developed to investigate the dynamic tensile fracture behaviour of concrete. On the meso-scale, concrete is regarded as a composite of aggregate, mortar and the interface transition zone (ITZ). The nucleation, coalescence, and propagation of cracks are modelled by pre-insert rate-dependent cohesive elements. Predicted results of the proposed numerical model fit well with experimental data in spall tests. The evolution of cracks in concrete under dynamic loading is explicitly presented. The micro-cracks of concrete are widely distributed before the initiation of macro-cracks. The results suggest that the inertia effect plays an important role in the dynamic fracture behaviour of concrete. Moreover, the influence of the mesostructure on the dynamic tensile strength is investigated. The dissipated fracture energy under dynamic loading is also indicated to be affected by the mesostructure of concrete.

The effect of coarse aggregate hardness on the fracture toughness and compressive strength of concrete

Coarse aggregate is the dominant constituent in concrete. Aggregate hardness is a variable needed to investigate in determining its effect on the critical stress intensity factors (KIC), dissipated fracture energy (Gf) and compressive strength (fc’) of the concrete. The hardness of coarse aggregate based on Los Angeles abrasion values of 16.7%., 22.6%, and 23.1% was used incorporated with Portland Composite Cement (PCC), and superplasticizer to create specimens. Cubes of 150x150x150 mm were employed to determine the fc’, and four beam sizes: 50x100x350 mm, 50x150x500 mm, 50x300x950 mm and 50x450x1250 mm were engaged to determine KIC and Gf. The fc’ and Gf of specimens manufactured by three different hardness of coarse aggregates were 45, 43, 40 MPa and 89.4, 54.0, 56.3 N/m respectively. KIC of specimens was 138.9, 119.4 and 114.1 MPa.mm1/2 for beam size of 50x100x350 mm; 148.2, 115.8 and 108.8 MPa.mm1/2 for beam size of 50x150x500 mm; 230.9, 183.1 and 157.9 MPa.mm1/2 for beam size of 50x300x950 mm; and 293.2, 248.1 and 244.3 MPa.mm1/2 for beam size of 50x450x1250 mm. Experimental results showed that decreasing hardness of coarse aggregate was found to have significant effect on the fracture toughness rather than on the compressive strength of concrete.

Dynamic Compression Damage Energy Consumption and Fractal Characteristics of Shale

Studying the relationship between energy consumption and crushed size of shale under different loading conditions is the key to efficient shale cracking. The split Hopkinson pressure bar system was used to study the dynamic mechanical properties of shale under parallel‐ and vertical‐bedding loading, and energy dissipation in the impact tests was calculated. Relationships between the average crushed size of shale fracture products and energy dissipation and between the fractal dimension and dissipated energy were studied using fractal theory. The experimental results showed that the dynamic compressive strength of shale under parallel‐ and vertical‐bedding conditions had an obvious positive correlation with the strain rate. Dissipative energy of the shale samples under loading in both directions increased with the increase of strain rate. The increase of the strain rate enhanced crushing of the sample. The vertical‐bedding shale samples had stronger ability to absorb energy and more internal crack propagation. Dissipative energies of the shale samples in the parallel‐ and vertical‐bedding impact tests were positively related to the fractal dimension. The fractal dimension increased with the increase of dissipative energy during sample failure; with further increase in the dissipative energy, its effect on the change of fractal dimension gradually weakened.

XFEM Simulation of Pore-Induced Fracture of a Heterogeneous Concrete Beam in Three-Point Bending

The extended finite element method with the linear softening law is employed to simulate poreinduced crack initiation and propagation in heterogeneous plain concrete beams in three-point bending. A series of numerical simulations was performed and experimentally validated. The crack was found to always initiate at the beam bottom in the point nearest to the pore, propagating through it. When the pore has a larger offset from the beam midspan, the beam displays higher fracture resistance and energy dissipation spent for fracture. With an increase in a distance from the beam bottom, the ultimate load also increases, but the energy dissipation slightly varies. The pore sizes have a little effect on the fracture resistance of the concrete beam.

3D Progressive Damage Based Macro-Mechanical FE Simulation of Machining Unidirectional FRP Composite

Finite element (FE) simulation is a powerful tool for investigating the mechanism of machining fiber-reinforced polymer composite (FRP). However in existing FE machining simulation works, the two-dimensional (2D) progressive damage models only describe material behavior in plane stress, while the three-dimensional (3D) damage models always assume an instantaneous stiffness reduction pattern. So the chip formation mechanism of FRP under machining is not fully analyzed in general stress state. A 3D macro-mechanical based FE simulation model was developed for the machining of unidirectional glass fiber reinforced plastic. An energy based 3D progressive damage model was proposed for damage evolution and continuous stiffness degradation. The damage model was implemented for the Hashin-type criterion and Maximum stress criterion. The influences of the failure criterion and fracture energy dissipation on the simulation results were studied. The simulated chip shapes, cutting forces and sub-surface damages were verified by those obtained in the reference experiment. The simulation results also show consistency with previous 2D FE models in the reference. The proposed research provides a model for simulating FRP material behavior and the machining process in 3D stress state.

Meshfree modeling of the dynamic mixed-mode fracture in FRC through an eigensoftening approach

This work is concerned with the numeric study of dynamic mixed-mode fracture in fiber reinforced concrete (FRC). A recently developed eigensoftening algorithm to deal with the fracture of quasi-brittle materials is employed in a meshfree framework. Three point bending tests on notched beams reinforced with steel fibers carried out through a drop weight device at two loading velocities are modelled. Since the notch was placed with an offset from the middle section, mixed-mode crack formation was facilitated. Assuming a linear softening stress-equivalent crack opening relation, the numerical methodology is first validated against experimental results on plain concrete. Subsequently, it is applied to study the dynamic fracture of fiber reinforced concrete with a newly-proposed bilinear relation. The studies reveal that the total fracture energy dissipation plays an important role on the peak reaction load, whereas the transitional point between the two branches has a significant influence on the crack patterns. Parametric studies on the notch position are also carried out. The results show that the notch position has a significant influence on the crack patterns.

Experimental and numerical investigation of the responses of scaled tanker side double-hull structures laterally punched by conical and knife edge indenters

This paper addresses experimental and finite-element simulation studies on scaled double-hull side structures quasi-statically punched at the mid-span by conical and knife edge indenters to examine their fracture behaviors and energy dissipation mechanisms. The specimen, scaled from a tanker double side, accounts for one span of the stringers in length and two spans of the web frames in width. The experimental results show that a double hull punched by a conical indenter shows much stronger resistance than that of a double hull punched by a knife edge indenter in severe collisions due to a difference in the fracture mode, while the double hull performs better in minor collisions punched by the knife edge indenter due to the deformation mode. In addition, numerical simulations are also carried out for the corresponding scenarios by the explicit LS-DYNA finite element solver. A relatively fine mesh in the contact area is used to capture the fracture initiation and propagation of the two specimens. The resistance-penetration curves and the deformations are compared with those observed in experiments, and these results match well. The numerical analysis discusses some aspects of particular relevance to the response of ship structures suffering accidental loads, including the importance of specifying the modeled welds, the influences of failure criteria, material relations on simulating complex structures, and application of scaling laws in assessing the impact response of full-scale structure.

Effect of Randomness of Interfacial Properties on Fracture Behavior of Concrete Under Uniaxial Tension

Interfacial transition zones (ITZs) between aggregates and mortar are the weakest parts in concrete. The random aggregate generation and packing algorithm was utilized to create a two-phase concrete model, and the zero-thickness cohesive elements with different normal distribution parameters were used to model the ITZs with random mechanical properties. A number of uniaxial tension-induced fracture simulations were carried out, and the effects of the random parameters on the fracture behavior of concrete were statistically analyzed. The results show that, different from the dissipated fracture energy, the peak load of concrete does not always obey a normal distribution, when the elastic stiffness, tensile strength, or fracture energy of ITZs is normally distributed. The tensile strength of the ITZs has a significant effect on the fracture behavior of concrete, and its large standard deviation leads to obvious diversity of the fracture path in both location and shape.

Phase-field modeling of anisotropic brittle fracture including several damage mechanisms

The present paper aims at modeling complex fracture phenomena where different damaging mechanisms are involved. For this purpose, the standard one-variable phase-field/gradient damage model, able to regularize Griffith’s isotropic brittle fracture problem, is extended to describe different degradation mechanisms through several distinct damage variables. Associating with each damage variable a different dissipated fracture energy, the coupling between all mechanisms is achieved through the degradation of the elastic stiffness. The framework is very general and can be tailored to many situations where different fracture mechanisms are present as well as to model anisotropic fracture phenomena. In this first work, after a general presentation of the model, the attention is focused on a specific paradigmatic case, namely the brittle fracture problem of a 2D homogeneous orthotropic medium with two different damaging mechanisms with respect to the two orthogonal directions. Illustrative numerical applications consider propagation in mode I and II as well as kinking of cracks as a result of a transition between the two fracture mechanisms. It is shown that the proposed model and numerical implementation compares well with theoretical and experimental results, allowing to reproduce specific features of crack propagation in anisotropic materials whereas standard models using one damage variable seem unable to do so.