Varying Volume Fractions Research Articles

Effect of γʹ distribution on the deformation behavior of alloy 718Plus - A phenomenological study of the dislocation-precipitate interaction mechanisms at room temperature and 650 °C

The effect of γʹ distribution on the deformation behavior of alloy 718Plus has been examined in specimens subjected to uniaxial tensile testing till fracture as well as interrupted at 1.8 % eng. strain at room temperature and 650 °C. The deformation mechanisms were studied in these specimens, comprising the unimodal (USTD and BSS) and the bimodal (BSD and USD) γʹ distributions with varying volume fractions of precipitates. The USTD specimen, containing a higher volume fraction of γʹ with smaller interparticle spacing, deformed through weakly coupled dislocation shearing. Conversely, in the BSS specimen, having a lower volume fraction of γʹ with larger interparticle spacing, predominant looping, and shearing by strongly coupled dislocations were observed. However, shearing of γʹ by strongly coupled dislocations was the prevalent mechanism of dislocation-particle interaction in the bimodal specimens, irrespective of the testing temperature. The bimodal USD specimen achieved over 20 % higher uniform elongation in contrast to the standard specimen (USTD) without any considerable reduction in strength, thus limiting the strength ductility trade-off. The bimodal specimens also sustained prolonged strain hardening prior to the onset of plastic instability, where the strain hardening behavior was found to be consistent with the nature of dislocation-precipitate interactions.

Pengaruh Penambahan Serat Pohon Bambu Ampel (Bambusa Vulgaris) pada Komposit Hybrid untuk Material Bumper Kendaraan Bermotor

Technological developments continue to increase in line with the times, producing various innovations that provide benefits to society, especially in the material sector. The use of a mixture of natural and synthetic fibers in composites (hybrid) has produced a stronger material, which can function as an alternative material for car bumpers. This research was carried out with the aim of determining the values ​​of impact toughness, tensile strength, and failure patterns that occur in the fracture cross section of the specimen through macro photographs. In this research, a hybrid composite was formed by combining ampelous bamboo fiber, fiberglass, and polyester resin. Variations in volume fraction applied include: 5%:25%:70%, 10%:25%:65%, and 15%:25%:60%. The specimens were formed according to ASTM E23 standards for impact tests and ASTM D638 for tensile tests. The results of the impact and tensile tests showed that the lowest value of impact toughness was 0.0744 J/mm² and tensile stress was 120.29 MPa. Meanwhile, the highest value for impact toughness was 0.0986 J/mm² and the tensile stress value was 147.65 MPa. Macro photo analysis of the fracture cross section is categorized as splitting in multiple areas and the fracture cross section also shows debonding and fiber pull out after the fracture occurred.

Study of the residual stress distribution in SiCp/Al composites under thermal cycling conditions

In this study, a three-dimensional random representative volume element model was constructed using the finite element method combined with Python script to investigate the residual stress distribution in SiCp/Al composites with varying volume fractions, particle shapes, and particle size under thermal cycling conditions. The model has two different particle morphologies: spheres and irregular polygons. The results show that the irregular polygonal SiC particles exhibit higher residual stresses than spherical particles before and after thermal cycling due to their complex load transfer pathways and higher stress concentration at particle corners, which makes them more consistent with the characterization of SiCp/Al composites under practical application conditions. As the volume fraction of SiC particles increases, the particle spacing decreases, hindering the release of thermal stresses through plastic deformation. Notably, the relief rate of residual stress reached 53% in the 12 vol% SiCp/Al composites, with the stress decreasing from 698 MPa to 328 MPa after 50 thermal cycles. In contrast, the reduction rate for 18 vol% composites is only 13% after thermal cycling. Furthermore, compared to larger particles (7.3 µm, 8.9 µm), the smaller particles (4.3 µm, 5.9 µm) exhibit a more uniform stress distribution and lower thermal stresses before and after thermal cycling. Consequently, our work provides a significant theoretical basis for the design and application of SiCp/Al composites, especially for the application of materials under extreme temperature changes.

Quantitative Equivalence and Performance Comparison of Particle and Field-Theoretic Simulations.

Particle and field-theoretic simulations are both commonly used methods to study the equilibrium properties of polymeric materials. Yet despite the formal equivalence of the two methods, no comprehensive comparisons of particle and field-theoretic simulations exist in the literature. In this work, we seek to fill this gap by performing a systematic and quantitative comparison of particle and field-theoretic simulations. In our comparison, we consider four representative polymeric systems: a homopolymer melt/solution, a diblock copolymer melt, a polyampholyte solution, and a polyelectrolyte gel. For each of these systems, we first demonstrate that particle and field-theoretic simulations are equivalent and yield exactly the same results for the pressure and the chemical potential. We next quantify the performance of each method across a range of different conditions including variations in chain length, system density, interaction strength, system size, and polymer volume fraction. The outcome of these calculations is a comprehensive look into the performance of each method and the systems and conditions when either particle or field-theoretic simulations are preferred. We find that field-theoretic simulations are equal to or faster than particle simulations for nearly all of the systems and conditions examined. In many situations, field-theoretic simulations are several orders of magnitude faster than particle simulations, especially if the polymer chains are long, the system density is high, and long-range Coulombic interactions are present. We also demonstrate that field-theoretic simulations are considerably faster at calculating the chemical potential and bypass the challenges associated with particle-based Widom insertion techniques. Taken together, our results provide quantitative evidence that field-theoretic simulations can reach and sample equilibrium considerably faster than particle simulations while simultaneously producing equivalent results.

Enhancing mixing characteristics of MgCl2 solution within atomization nozzles: A computational fluid dynamics investigation of structural parameter

Efficient dispersion of MgCl2 solution is crucial in saline lake industries. Understanding how structural variables influence atomization can improve nozzle design. This study uses Computational Fluid Dynamics (CFD) modeling to examine the effects of key structural parameters on MgCl2 solution mixing in atomization nozzles. It focuses on the impact of liquid injection hole size, number of air injection holes, and mixing chamber length on the nozzle's fluid dynamics. The analysis covers variations in internal velocity and MgCl2 volume fraction. Simulations show that increasing the liquid injection hole diameter reduces liquid flow resistance, while adding more air injection holes leads to a more uniform air distribution, though with a slight increase in atomization efficiency. A longer mixing chamber reduces gas phase velocity. Optimal mixing efficiency is achieved with 4 air injection holes, a 1.5 mm liquid injection hole, a 7 mm mixing chamber, a 2 mm nozzle outlet, 0.3 MPa inlet gas pressure, and an 80 L/h solution flow rate. This study provides insights into key parameters for improving performance and refining industrial applications.

Turbulent convection in emulsions: the Rayleigh–Bénard configuration

This study explores heat and turbulent modulation in three-dimensional multiphase Rayleigh–Bénard convection using direct numerical simulations. Two immiscible fluids with identical reference density undergo systematic variations in dispersed-phase volume fractions, $0.0 \leq \varPhi \leq 0.5$ , and ratios of dynamic viscosity, $\lambda _{\mu }$ , and thermal diffusivity, $\lambda _{\alpha }$ , within the range $[0.1\unicode{x2013}10]$ . The Rayleigh, Prandtl, Weber and Froude numbers are held constant at $10^8$ , $4$ , $6000$ and $1$ , respectively. Initially, when both fluids share the same properties, a 10 % Nusselt number increase is observed at the highest volume fractions. In this case, despite a reduction in turbulent kinetic energy, droplets enhance energy transfer to smaller scales, smaller than those of single-phase flow, promoting local mixing. By varying viscosity ratios, while maintaining a constant Rayleigh number based on the average mixture properties, the global heat transfer rises by approximately 25 % at $\varPhi =0.2$ and $\lambda _{\mu }=10$ . This is attributed to increased small-scale mixing and turbulence in the less viscous carrier phase. In addition, a dispersed phase with higher thermal diffusivity results in a 50 % reduction in the Nusselt number compared with the single-phase counterpart, owing to faster heat conduction and reduced droplet presence near walls. The study also addresses droplet-size distributions, confirming two distinct ranges dominated by coalescence and breakup with different scaling laws.

Biomechanical assessment of zirconia-calcium silicate-silver composite dental crowns: A 3D finite element analysis study

Optimal dental health significantly contributes to an individual’s physical and psychological well-being, with an increasing focus on esthetics and functionality in dental restoration procedures. This research explores the use of zirconia ceramic materials combined with calcium silicate and silver compositions as an alternative for dental crown applications. The study employs 3D finite element analysis to assess stress distribution on full crowns with composites under axial and oblique loads, aiming to understand biomechanical aspects and identify fracture resistance and failure modes. The materials include zirconia-calcium silicate-silver composites with varying volume fractions (Zr 74 to 29%, Ca2SiO4 68 to 25%, and Ag 3 to1%). Results show stress concentration at the crown intaglio surface, influenced by the material’s elastic modulus. Specifically, the C14 composite crown with Young’s modulus 90.82 GPa exhibits lower stress levels for crown 10.9 MPa at axial load and 12.77 MPa at oblique load, making it a potentially recommended choice. These findings suggest the potential of designed biomaterials, emphasizing the importance of material selection in enhancing the longevity and resilience of dental crowns. Also, the study enhances understanding of biomechanical aspects in dental crown restorations, contributing valuable insights for clinical applications.

Phase velocity of love waves as function of heterogeneity and void parameter

The present study looks at the Love wave propagating through an elastic layer containing empty pores situated above a heterogeneous elastic semi-infinite space. We have constructed separate formulations of equations of motion for both media under congruous boundary conditions. The separation of variables approach is used to build the phase velocity frequency relation in compact form using the Whittaker function. The resulting closed-form dispersion equation matches the conventional Love wave equation when heterogeneity has been removed. The propagation of Love waves is strongly influenced by a porous layer of limited thickness across an elastic semi-infinite space. Three wave fronts are demonstrated to have the potential to propagate. The equilibrated inertia and the variation in the void volume fraction are related to two wave fronts that are connected to the characteristics of the void pores. Numerical treatments are applied and graphically illustrated to implement these effects associated to Love waves’ phase velocity.

Analysis of heat transfer coefficient in radiator cooling system using TiO2/CuO hybrid fluid

The automotive industry is growing, encouraging more efficient car cooling systems, especially radiators. Innovations are constantly being made to improve the performance of radiators. Choosing the correct fluid is one of the ways to increase heat transfer. This study aimed to compare the performance of coolant OBC and TiO2/CuO hybrid fluid mixed with coolant OBC to investigate the increase in heat transfer in the car's radiator. The first step is to make TiO2/CuO hybrid fluid with a two-step method, with volume fraction variations of 1.0, 2.0, 3.0, 4.0, and 5.0%, and observe stability for 30 days. Viscosity and thermal conductivity tests are used to assess the thermophysical properties of the sample. Hybrid fluid samples of TiO2 / CuO with a volume fraction of 5.0% showed the best stability and thermal conductivity, then were added to the coolant brand OBC (1:4). The results showed an increase in heat transfer rate of 23% and a heat transfer coefficient of 20% in the TiO2/CuO hybrid fluid added to the coolant OBC

Effect of dual NEPCM and tapered fins on thermal runaway control in lithium-ion batteries

This research investigates the thermal performance of dual phase change materials (PCMs) RT82 (PCM1) and RT27 (PCM2) using tapered fins and nanoparticles to improve their thermal management capabilities, specifically for controlling excessive heating in lithium-ion battery cells. The primary objective is to enhance heat transfer efficiency and melting characteristics of dual PCMs by incorporating alumina (Al2O3), molybdenum disulfide (MoS2), and single-walled carbon nanotubes (SWCNTs) nanoparticles at varying volume fractions and configuring tapered fins in different arrangements. A series of parametric studies were conducted to analyze the impact of these modifications on the thermal transport and solid-liquid transition characteristics of the PCMs. The key findings indicate that the incorporation of nano-sized particles significantly enhances the thermal conductivity of PCMs, with SWCNTs showing the highest improvement. The PCM system with 6 % SWCNTs nanoparticles exhibited a 41.85 % increase in melting characteristics compared to the baseline PCM. The study also reveals that increasing the number of fins from two to eight results in a 94.28 % increase in the melting rate for RT82 and a 50 % increase for RT27. Furthermore, the combination of increased nanoparticle concentration and fin number leads to a 12.17 % rise in melt pool temperature distribution for 2 % SWCNTs and 14.08 % for 6 % SWCNTs. The enhanced thermal conductivity and efficient heat transfer due to the synergistic effect of fins and nanoparticles result in faster phase transitions and improved temperature regulation within the system. These findings underscore the potential of optimized PCM configurations with advanced materials for superior thermal management solutions in high-heat applications, effectively extending the operational efficiency and lifespan of thermal systems like lithium-ion batteries.

Influence of mixed particle sizes on shear yield stress of magnetorheological fluid

AbstractThis study investigated the effect of magnetic particle size and volume fraction on the shear yield stress and dynamic viscosity of magnetorheological fluids. Magnetorheological fluids with varying volume fractions of micro‐ and nanoscale magnetic particles were prepared. A plate‐on‐plate shear test bench was constructed to evaluate the fluids under a constant shear rate, with the applied current ranging from 0 A to 1.2 A. Results indicated that the shear yield stress initially increased and then decreased as the volume fraction of magnetic nanoparticles increased, reaching a maximum of 47 kPa at a volume fraction of 7 %. However, the excessive addition of magnetic particles or large‐diameter particles led to settling and reduced stability of the fluids. The findings suggest that optimizing the size and volume fraction of magnetic particles is crucial for maximizing the shear yield stress of magnetorheological fluids.

On the stability of coherent HfRu- and ZrRu-B2 precipitates in Nb-based alloys

High temperature creep strengths of Nb-based alloys have been limited by the lack of coherent precipitates that exist at temperatures above 1200▪. In this investigation, a series of BCC Nb-based alloys with coherent HfRu- and ZrRu-B2 precipitates were investigated to determine the dependence of phase stability, misfit, and solvus temperatures on composition. Sequential anneals from 1000-1500▪ were used to determine the B2 solvus temperature (Ts,B2) of each alloy and solvus lines were constructed for each system. HfRu-B2 is found to be more thermally stable than ZrRu, with HfRu-containing alloys demonstrating higher Ts,B2 at equivalent Ru concentrations. For alloys with Ts,B2 above 1200▪, additional anneals at 1000 and 1200▪ provide insight into B2 volume fraction variations with temperature. Additional Hf- and Zr-rich tertiary phases also formed on the grain boundaries of the selected compositions at intermediate to high temperatures. Through transmission electron microscopy, the lattice misfits for the B2 precipitates were found to be ≈ 0.5% at 1000▪ and the grain boundary phases were identified as C14 Laves, L10, β-Hf, and topologically close-packed P phases. Implications for the design of Nb-based alloys strengthened by Ru-B2 precipitates, including strategies to mitigate deleterious phase formation, are discussed throughout.

Experimental and machine learning study on the influence of nanoparticle size and pulsating flow on heat transfer performance in nanofluid-jet impingement cooling

Maximizing heat transfer efficiency is crucial for enhancing performance and durability in diverse engineering applications, including fuel cells, EV batteries, and solar PV/T systems, thereby advancing sustainable energy innovation. This study investigates thermal dissipation from a simulated heat sink aligned with a PV cell’s back plate via jet impingement cooling. Specifically, it examines the impacts of pulsatile cooling and nanoparticle size in hybrid nanofluids, comprising combinations of Al2O3 and MWCNT in water, with varied nanofluid volume fraction (0.05 vol% ≤ ɸ ≤ 0.3 vol%) and flow Reynolds number (15000 < Re < 40000). Key findings reveal significant influences of nanoparticle size, nanofluid concentration, and pulsating flow on heat transfer performance. Notably, sample D demonstrated the highest heat transfer enhancement, achieving approximately 52.94 % and 79.06 % improvement in continuous and pulsating jet cooling compared to de-ionized water under continuous jet cooling. Machine learning classifiers were employed to identify critical thermal performance parameters, with Reynolds number identified as the most significant factor influencing heat transfer. Random Forest and Gradient Boosting classifiers showed notable accuracy in predicting Nu, emphasizing the role of machine learning techniques in optimizing thermal management strategies for improved heat dissipation from solar PV cell backplates.

Extending the Natural Neighbour Radial Point Interpolation Meshless Method to the Multiscale Analysis of Sandwich Beams with Polyurethane Foam Core

This work investigates the mechanical behaviour of sandwich beams with cellular cores using a multiscale approach combined with a meshless method, the Natural Neighbour Radial Point Interpolation Method (NNRPIM). The analysis is divided into two steps, aiming to analyse the efficiency of NNRPIM formulation when combined with homogenisation techniques for a multiscale computational framework of large-scale sandwich beam problems. In the first step, the cellular core material undergoes a controlled modification process in which circular holes are introduced into bulk polyurethane foam (PUF) to create materials with varying volume fractions. Subsequently, a homogenisation technique is combined with NNRPIM to determine the homogenised mechanical properties of these PUF materials with different porosities. In this step, NNRPIM solutions are compared with high-order FEM simulations. While the results demonstrate that RPIM can approximate high-order FEM solutions, it is observed that the computational cost increases significantly when aiming for comparable smoothness in the approximations. The second step applies the homogenised mechanical properties obtained in the first step to analyse large-scale sandwich beam problems with both homogeneous and functionally graded cores. The results reveal the capability of NNRPIM to closely replicate the solutions obtained from FEM analyses. Furthermore, an analysis of stress distributions along the beam thickness highlights a tendency for some NNRPIM formulations to yield slightly lower stress values near the domain boundaries. However, convergence towards agreement among different formulations is observed with mesh refinement. The findings of this study show that NNRPIM can be used as an alternative numerical method to FEM for analysing sandwich structures.

Investigating the mechanical properties of composites containing exfoliated graphite/epoxy sensors: Experimental testing and simulation

One approach to structural health monitoring (SHM) involves embedding sensors within a composite material. However, the integration of these sensors can potentially introduce flaws that might affect the composite’s mechanical properties. This research aims to explore the impact of embedding exfoliated graphite (EG)/epoxy sensors on the mechanical characteristics of composite systems through laboratory experiments and numerical simulations. Sensor strips composed of varying volume fractions of EG/epoxy were fabricated. Tensile test specimens were prepared by embedding these sensors in the epoxy matrix oriented both lengthwise and widthwise. Baseline specimens of EG/epoxy without sensors were also created for comparison. Tensile tests were performed on the samples to evaluate the effects of the embedded sensors on the composite’s elastic modulus and tensile strength. The results indicated a slight improvement in both elastic modulus and tensile strength with the introduction of EG. Crucially, the orientation of the sensors within the samples had a significant impact on the composite’s mechanical properties. Samples with widthwise-aligned sensors showed reduced tensile strength due to delamination along the sensor edges. Finite element simulations using a viscoelastic model based on the experimental data were conducted to analyze the effect of sensor alignment on mechanical properties. The findings revealed that a grid pattern alignment of sensors significantly enhanced mechanical performance compared to lengthwise or widthwise alignment, particularly at 0.1% and 0.3% EG volume fractions, highlighting the effectiveness of a grid pattern for embedding sensors in SHM applications.

A Three-Dimensional Modeling Approach for Carbon Nanotubes Filled Polymers Utilizing the Modified Nearest Neighbor Algorithm.

Carbon nanotubes (CNTs) are extensively utilized in the fabrication of high-performance composites due to their exceptional mechanical, electrical, and thermal characteristics. To investigate the mechanical properties of CNTs filled polymers accurately and effectively, a 3D modeling approach that incorporates the microstructural attributes of CNTs was introduced. Initially, a representative volume element model was constructed utilizing the modified nearest neighbor algorithm. During the modeling phase, a corresponding interference judgment method was suggested, taking into account the potential positional relationships among the CNTs. Subsequently, stress-strain curves of the model under various loading conditions were derived through finite element analysis employing the volume averaging technique. To validate the efficacy of the modeling approach, the stress within a CNT/epoxy resin composite with varying volume fractions under different axial strains was computed. The resulting stress-strain curves were in good agreement with experimental data from the existing literature. Hence, the modeling method proposed in this study provides a more precise representation of the random distribution of CNTs in the matrix. Furthermore, it is applicable to a broader range of aspect ratios, thereby enabling the CNT simulation model to more closely align with real-world models.

A micromechanics-based artificial neural networks model for rapid prediction of mechanical response in short fiber reinforced rubber composites

The complex microstructural characteristics inherent in short fiber reinforced rubber composites (SFRRCs) impose considerable computational burdens in predicting the mechanical behavior of such composite materials. To address this challenge, this research extends the applicability of the homogeneous model predicated on the orientation averaging method to encompass composite materials featuring hyperelastic matrices. Combined with finite element method, a comprehensive mechanical response database encompassing various volume fractions and fiber orientation distributions is established. Leveraging this database, a micromechanics-based artificial neural network (ANN) model is meticulously designed to rapidly predict the mechanical response of SFRRCs across varying volume fractions and fiber orientation distributions, utilizing a fixed strain step strategy. To ascertain the efficacy and precision of the developed ANN model, representative volume elements portraying both planar and three-dimensional random distributions of composites are constructed and subjected to finite element analysis. Results indicate that the predicted outcomes from the ANN model align closely with finite element calculations within a certain strain range, while significantly reducing computational costs.

Coupled torsion and inflation of functionally graded and residually stressed Mooney–Rivlin hollow cylinders

Functionally graded structures have material properties continuously varying in one or more directions. Examples include human teeth, sea shells, bamboo stems, and mammal organs in which the varying volume fraction and orientation of fibers optimize their functionalities. Here we analytically study large deformations due to combined torsion and inflation of residually stressed and radially graded Mooney–Rivlin hollow circular cylinders to provide insights into how grading their material moduli according to a power law function of the radius can be advantageously used. We simulate residual stresses in a thin wall hollow cylinder by inverting it inside out and in a thick wall cylinder by assuming that a longitudinal wedge opening parallel to the cylinder axis is closed by deforming it axisymmetrically. It is found that positive integer values of the power law exponent are generally advantageous but its negative values can have deleterious effects on stress distributions. Furthermore, a hollow cylinder with residual stresses generated by one of the foregoing methods in the reference configuration should be modeled as orthotropic rather than transversely isotropic for subsequent deformations. The analytical solutions provided here should help numerical analysts verify their algorithms for large deformations of rubber-like materials that are modeled by the Mooney–Rivlin relation, and design engineers for exploiting the radial gradation of the two material moduli to reduce structure’s mass without sacrificing its performance.

Investigation of the insoluble impurities' impact on flow boiling heat transfer in aluminum microchannel heat exchangers

Microchannel flat-tube heat exchangers are known for their high heat transfer efficiency and compact size. In practical applications, the predominantly adverse influence of insoluble impurities on the condensation process necessitates further exploration into the underlying mechanisms affecting the flow boiling process. The effect of common insoluble impurities on the flow boiling of R410A refrigerant in a microchannel flat-tube heat exchanger has been investigated, and variation of the impurity volume fraction on heat transfer, mass transfer, pressure drop, and bubble formation are analyzed. Additionally, an adaptive modification method for the mass transfer factor is proposed. The numerical model of flow boiling heat transfer in a microchannel is validated through experimental data and empirical correlations. Thermo-hydraulic performance evaluation incorporates efficiency index and area goodness ratio metrics. Results reveal that the presence of insoluble impurities complicates the boiling heat transfer mechanism by influencing bubble evolution and multiphase flow patterns. Air impurities at a volume fraction not exceeding 5% prove beneficial for enhancing flow boiling efficiency in microchannels; however, a 38.5% decrease in efficiency index is observed with 1% oil impurities present. Optimal thermo-hydraulic performance is achieved with approximately 2%–3% water impurities.

Sifat Mekanik Komposit Serat Pelepah Kelapa Sawit sebagai Penguat Komposit Terhadap Kekuatan Tarik dan Impak

Palm fronds are solid waste from oil palm plantations that contain a lot of natural fibers. One of the utilization efforts that can be done is to optimize palm frond fiber waste into composite materials. The use of natural fiber mixtures in composites has produced stronger materials, which can serve as alternative materials for car bumpers. This research was conducted with the aim of knowing the value of impact toughness, tensile strength, and the type of failure that occurs in the fracture cross section. In this study, composites were made using palm frond fibers and polyester resin. The volume fraction variation applied is 30% fiber and 70% matrix with fiber lengths of 20 mm, 40 mm, and 60 mm. Impact toughness testing refers to ASTM E23 standard and tensile strength testing refers to ASTM D638 standard. The impact toughness value obtained in the 20 mm variation was 0.0065 J/mm², 40 mm was 0.0108 J/mm², and the 60 mm variation had the highest value of 0.0164 J/mm². The tensile strength value obtained in the 20 mm variation is 6.18 MPa, the 40 mm variation is 8.26 MPa, and the 60 mm variation has the highest value of 16.45 MPa. Analysis of the fracture cross section is categorized as a splitting fracture in multiple areas and the fracture cross section also shows the occurrence of fiber pull out after the fracture.