Interfacial Shear Force Research Articles

(Invited) Design of Reduced Shear Force Cu Cleaning Processes Via α-β-Unsaturated Chemistries for Enhanced BTA Residue Removal

As integrated circuit and logic devices continue to decrease, limiting induced defectivity during Chemical Mechanical Planarization (CMP) processes (polishing and substrate cleaning) is imperative. Defects resulting from the CMP process can be classified as mechanical (i.e., scratching), chemical (i.e., corrosion), or physiochemical (i.e., adsorbed contaminants) according to the mechanism of formation. Traditionally, a contact cleaning method implements a polyvinyl alcohol (PVA) brush to transfer cleaning chemistry to the substrate of interest and provides the necessary mechanical energy for defect removal. While this process effectively removes contaminants, its reliance on shear forces can induce secondary defect modes, such as scratching. One major challenge for the post-CMP cleaning of Cu substrates is the polymeric residue film comprised of BTA-Cu+ complexes that propagate during the CMP polishing process. The current and most effective mode to mitigate this “residue defect” is coupling brush-induced shear force with additives that promote interfacial redox reactions to remove residues through an undercutting mechanism. This work focuses on developing a “softer” and additive structure-based approach that drives less aggressive interfacial shear between the brush and wafer substrate. More specifically, α-β-unsaturated additives with diverse functionality (i.e., -unsaturated carboxylic acids, carboxylic acids, and unsaturated benzaldehydes) will be tested to evaluate their efficacy to “overcut” the organic residue via a proposed aza-Michael addition reaction pathway. This “overcutting” mechanism relies on additional modes of interaction (i.e., p-stacking, H-bonding, conformational relationships, etc.) with the BTA- Cu+ polymeric residue film. A suite of dynamic techniques (i.e., Tafel analysis, OCP vs. time, contact angle, additive diffusion analysis, and shear force) will attempt to correlate the additive structure and reaction mechanism to organic residue removal efficiency and measured interfacial shear forces. Initial results have shown that implementing an “overcutting” mechanism will decrease the overall shear force and significantly reduce the generation of secondary defects without sacrificing overall defect removal efficiency.

Experimental and numerical analyses on the shear behavior of grouped single-embedded-nut high-strength bolts in steel–ultra-high-performance concrete composite slabs

Incorporating utilization of ultra-high-performance concrete (UHPC) slabs and single-embedded-nut high-strength bolts (SENHSBs) can optimize the structural performance and construction efficiency of steel–concrete composite slabs. Typically, SENHSBs are required to be densely arranged in groups to transfer sufficient interfacial shear forces in complex stress regions. However, the investigations focused on the performance of grouped SENHSBs embedded in UHPC slabs is limited. Against this background, 15 push-out tests were conducted, accompanied by comprehensive numerical analyses, to study the shear behaviors of grouped SENHSBs in steel–UHPC composite slabs. The test results demonstrated that the failure model was governed by SENHSB fracture. Specimens with the longitudinal spacing of twice the bolt diameter exhibited overlapping crushing areas in the UHPC slabs. The longitudinal spacing significantly influenced both the ultimate shear and ultimate slip capacities of the grouped SENHSBs, whereas the transverse spacing significantly affected both the shear stiffness and maximum slip of grouped SENHSBs. Additionally, the per bolt ultimate shear capacities of the specimens with multi-layer SENHSBs were significantly lower than those with single-layer SENHSBs. The SENHSBs located at various positions experienced different shear stresses, and the deviations became more significant as the longitudinal spacing decreased. Consequently, a formula was proposed to evaluate the strength reduction factor of the grouped SENHSBs. Furthermore, accurate models were developed for determining the ultimate shear capacity and load–slip relationship of grouped SENHSBs in steel–UHPC composite slabs.

Study on reasonable anchorage length based on failure mechanism of the bolt anchorage system

In addition to analysing the mechanism of failure of the prestressed rock anchor anchor system and investigating the appropriate depth for fixing the rock anchors, theoretical equations were derived to calculate the rock anchors' axial force, ultimate capacity, and the interfacial shear force in the elastic phase. These equations are then used to analyse the pressure distribution within the rock bolt anchorage section and to investigate the effect of interfacial shear strength, shear stiffness, and anchorage length on interface failure. Drawing on the findings from both field-based rock bolt pull-out tests and numerical simulations, analyzed the failure mechanism of the anchor system, and proposed a reasonable anchor length design method for rock bolt. The results show that there is a strong dependence between ultimate load carrying capability of rock bolts and interfacial shear stress and shear rigidity, and that increasing the anchorage length and reducing the interface shear stiffness can avoid the stress concentration phenomenon. The primary factor leading to the anchor system failure is secondary interface failure. The evolution law of interface damage is that the damage occurs first at the initial position. As the interface damage location changes, the peak shearing stress moves towards the bottom of the anchored section. The engineering application results verified the feasibility of a reasonable anchorage length calculation method and rock bolt design process. The findings of this paper can be used as a basic reference for determining rock bolt anchorage support parameters during the design and construction of underground engineering projects.

Load Transferring Characteristics of Expanded Pile with Cement Mortar Mixture for Pipe Pile

Two kinds of interface shear force transmission models of expanded pile are introduced in combination with FRIC subroutine. ABAQUS is used to carry out numerical analysis to study the load transfer characteristics of expanded pile under vertical load. The results show: the load on the top of the pile is transmitted by the strong cohesive force between the pipe pile and the expanded interface. Under the vertical load, the axial stress of the pipe pile in the expanded pile gradually decreases with the increase of depth, and the axial stress of the expanded part increases first and then decreases with the depth. With the increase of pile length, pipe pile diameter or expansion thickness, the axial stress of pipe pile increases as a whole. With the increase of pile length, the axial stress of the expansion body increases gradually, and with the increase of pile diameter or expansion thickness, the axial stress of the expansion body decreases gradually. The axial stress of the pipe pile in the equal core part of the non-equal core expanded pile gradually decreases with the increase of depth, and the axial stress of the expanded body increases with the increase of the pile length.

Construction and Properties of High-Toughness Soft-Soft Interfaces Based on the Adhesion of Natural Polyphenols.

Artificial joint replacement is the most effective way to treat osteoarthritis. However, these artificial joints are too stiff with high interfacial contact stress and poor surface lubrication, resulting in stress shielding and severe wear and tear lead to an extremely high failure rate. At present, hydrogels are considered the most promising substitute for artificial joint prostheses owing to their good biocompatibility, adjustable mechanical properties, and excellent flexibility. Nevertheless, a traditional single-layer hydrogel has poor bearing capacity and lubrication, which are far from the properties of natural articular cartilage. The high strength and low friction properties of natural articular cartilage are based on its own multilayer fibrous structure. Therefore, by simulating the multilayer structure of natural cartilage, a bilayer bionic cartilage hydrogel was prepared; that is, the upper hydrogel realized excellent lubrication and the lower hydrogel realized high load-bearing capacity. However, the interface binding of bilayer hydrogels is a challenge at present. Therefore, the interfacial adhesion of the bilayer hydrogel is improved by adding tannic acid (TA) based on the adhesion of the natural polyphenol structure. The average interfacial toughness reaches 3650 J/m2, and the average interfacial shear force reaches 800 kPa. In the preparation of the bilayer hydrogel, taking advantage of the coordination reaction between TA and metal cations, Fe3+ is further added to endow the bilayer hydrogel with excellent mechanical properties and good sliding friction performance. Therefore, this work opens up a new way to construct cartilage-like materials with high toughness and a soft-soft interface.

Experimental study of shear-driven water film with brightness-based laser-induced fluorescence technique

Driven by low-temperature and high-speed airflow, the water droplets impinging the surface of the aircraft will gather into water film, affecting the aerodynamic characteristics and endangering flight safety. In this paper, a high-speed video system with the brightness-based laser-induced fluorescence (BBLIF) technique was used to analyze the transient water film thickness and wavy characteristics on a horizontal metal plate. A series of experiments were performed over a wide range of wind speeds (15.59 m/s ∼ 52.20 m/s) and water volume flow rates (100 ml/min ∼ 900 ml/min). According to the interfacial phenomena observed in the experiment, the water film flow is classified into five regimes: two-dimension-wave, ripple-wave, dual-wave, roll-wave, and entrainment. The water film characteristics such as mean film thickness, film roughness, wave frequency, and rolling wave intermittency are studied under the influences of air velocity and water flow rate. The results show that the complex fluctuation characteristics of water film are the result of the joint action of surface tension, interfacial shear force and inertia term of water film, and are closely related to the water film flow regime. The findings could contribute to a better understanding of the shear-driven water film wavy characteristics and the optimization of the anti-icing or de-icing system.

Sustainable green reinforcement engineering: High-performance GTRM reinforced composites with interfacial gradient structure

Building reinforcement projects are designed to meet the requirements of modern sustainable development. However, the weak bonding performance of continuous glass fiber textiles to mortar presents a challenge in the manufacturing of GTRM composites, hindering their development and application. In this study, the gradient composite design technique was used to modify the interface transition zone between continuous glass fiber textile and mortar by introducing epoxy resin. This successfully resolved the issue of poor bonding between the continuous glass fiber textile and mortar interface, and promoted effective stress transfer between the two materials. The GTRM composites with an interfacial gradient structure exhibit excellent mechanical properties, including a tensile strength of 8 MPa and an interfacial shear force exceeding 27 KN. In addition, digital image correlation (DIC) was utilized to investigate the growth and development of cracks in GTRM composites, and the failure mechanism of tensile and interfacial shear tests was analyzed. Finally, the externally bonded GTRM composites were subjected to a three-point bending test, which demonstrated a significant improvement in the flexural strength and crack resistance of concrete beams.

Kinetic analysis of a freely rising droplet in water during collision with the horizontal wall

An in-depth analysis of the kinetics of the collision between freely rising oil droplets in water in the range of Re = 4.64–463.3 was carried out to understand the physical mechanism and detailed kinetics of the interaction between the oil droplets and wall. The results show that when oil droplets with Re ≥ 27.8 hit the wall vertically at terminal velocities, a “dimple-like” water film is formed near the wall, which significantly affects the pressure distribution within the water film, the oil–water interfacial shear force, and forces on oil droplet. A coupled model describing water film thickness and pressure accurately captures the kinetic behavior of water film drainage near the wall. The film-induced force based on lubrication theory can reasonably predict the motion trajectory of oil droplets near the wall and dominate the motion of oil droplets colliding with the wall. The motion phase diagram with (Re, We) as the control parameter was established to quickly identify the droplet motion rule under different liquid–liquid density ratios.

Prediction of interfacial shear strength of CNT overwrapped carbon fibers using molecular dynamics and Fourier series decomposition of surface asperities

ABSTRACT This paper aims to develop a novel approach to determining the fiber/matrix interfacial shear strength (IFSS) due to both carbon fiber roughness and the presence of carbon nanotubes (CNTs) in the matrix of a polymer composite in the form of a fiber overwrap. Under an atomic force microscope (AFM), the carbon fiber surface exhibits multi-scale asperities extending from a nanometer to several microns, likely caused by shrinkage during the graphitization process. Therefore, a Fourier series decomposition of the surface asperity data is performed to model these asperities present at various wavelengths on the fiber resulting in an amplitude and wavelength corresponding to each Fourier series term, effectively capturing the surface roughness over the entire spectrum of wavelengths. Furthermore, Molecular Dynamics (MD) simulations were performed to determine the interfacial shear strength of any subcomponent asperity of a specific amplitude and wavelength. Using MD data, governing equations were developed to compute the length-scale-averaged shear strength for a carbon fiber with any given surface asperities from the interfacial shear force for each of these subcomponent wavelengths. The results show that the presence of CNTs enhanced the IFSS by about 19% overall for a given surface asperity profile compared with the case without CNTs.

Solvent Volatilization-Induced Cross-Linking of PDMS Coatings for Large-Scale Deicing Applications

Icing of surfaces has become a serious issue, and effective methods for preventing ice accretion have received much attention in recent years. Here, a solvent volatilization-induced cross-linking hydroxy-terminated dimethylsiloxane (Si–OH) coating with tetramethoxysilane (TMOS) as a cross-linker is proposed for large-scale deicing applications. Interfacial adhesion tests and shear force analysis were conducted to confirm the large-scale deicing properties of the polydimethylsiloxane (PDMS) coating. Through characterization of morphology, it was found that there were negative correlations between roughness and constant shear force and shear strength. The mean constant shear force per unit width could be lower than 14 N/cm when the roughness was in the highest range fabricated in this research. In addition to the morphology of the surface, the mass ratio of the cross-linker to the premonomer affected the state of the surface and the deicing properties. When the mass ratio was lowered, uncross-linked molecular chains of the premonomer existed on the surface, which resulted in an increase in interfacial toughness and a reduction in shear strength. Finally, durability tests showed that the coating had excellent durability and could endure at least 50 cycles without an apparent increase in the constant shear force.

Relation between interfacial shear and friction force in 2D materials.

Understanding the interfacial properties between an atomic layer and its substrate is of key interest at both the fundamental and technological levels. From Fermi level pinning to strain engineering and superlubricity, the interaction between a single atomic layer and its substrate governs electronic, mechanical and chemical properties. Here, we measure the hardly accessible interfacial transverse shear modulus of an atomic layer on a substrate. By performing measurements on bulk graphite, and on epitaxial graphene films on SiC with different stacking orders and twisting, as well as in the presence of intercalated hydrogen, we find that the interfacial transverse shear modulus is critically controlled by the stacking order and the atomic layer-substrate interaction. Importantly, we demonstrate that this modulus is a pivotal measurable property to control and predict sliding friction in supported two-dimensional materials. The experiments demonstrate a reciprocal relationship between friction force per unit contact area and interfacial shear modulus. The same relationship emerges from simulations with simple friction models, where the atomic layer-substrate interaction controls the shear stiffness and therefore the resulting friction dissipation.

Local Shearing Force Measurement during Frictional Sliding Using Fluorogenic Mechanophores.

When two macroscopic objects touch, the real contact typically consists of multiple surface asperities that are deformed under the pressure that holds the objects together. Application of a shear force makes the objects slide along each other, breaking the initial contacts. To investigate how the microscopic shear force at the asperity level evolves during the transition from static to dynamic friction, we apply a fluorogenic mechanophore to visualize and quantify the local interfacial shear force. When a contact is broken, the shear force is released and the molecules return to their dark state, allowing us to dynamically observe the evolution of the shear force at the sliding contacts. We find that the macroscopic coefficient of friction describes the microscopic friction well, and that slip propagates from the edge toward the center of the macroscopic contact area before sliding occurs. This allows for a local understanding of how surfaces start to slide.

Visualization experiment and numerical simulation on behaviors of gas-liquid falling film flow on the air-side of two-row plain finned-tube heat exchanger

The frost-free air-source heat pump (ASHP) with integrated liquid desiccant dehumidification is a more promising energy-saving alternative to the conventional ASHP unit. The performance of spray-type finned-tube heat exchanger (FTHE), as one of the key equipment of this frost-free ASHP system, is affected by a combination of various factors including wall wettability, liquid film flow pattern, liquid film thickness, velocity distribution in a liquid film, interface wave, interface velocity and so on. To provide a theoretical basis for the operation, design and optimization of high-performance spray-type FTHE, a visualization experiment system and a three-dimensional (3D) numerical model are employed to study the behaviors of counter-current gas-liquid falling film flow on the air-side of two-row plain FTHE under different parameters in the present paper. According to the experimental results, the flow pattern of liquid film on the finned-tube surface is a mixture flow composed of the rivulet flow and the thin falling film flow, demonstrating that the assumption of the uniform distribution for liquid film thickness proposed in previous studies is not completely consistent with the actual situation. Meanwhile, the numerical results indicate that the transient-average film thickness on the surface of two-row plain finned-tube is significantly 18.3% – 32.5% higher than that on the vertical plate calculated by Nusselt's model. After that, the critical gas and liquid Reynolds numbers of the flow pattern transition for the liquid film are obtained, and it is pointed out that the wall contact angle of 10° is more conducive to the formation of complete film flow on the air-side of the two-row plain FTHE within the fin pitch range of 4.8 – 6.0 mm. The changes of the falling liquid film and gas-liquid interface characteristics are fundamentally attributed to the drag effect of the interfacial shear force. Furthermore, there is a cubic curve relationship between average interface shear force and gas Reg. A quadratic curve relation exists between average wall shear stress and gas Reg. At the same time, the velocity of falling film fluid at the bottom region of laminar flow is reduced, resulting from the inhibiting effect of the interfacial shear force.

DEM investigation of shear mobilisation during tyre strip pull-out test

This paper presents an evaluation of the pull-out behaviour of tyre strip-reinforced granular soil. The three-dimensional discrete element method (3D DEM) and laboratory testing were used to systematically calibrate the soil particles and the tyre strip based on their stress-strain relationship, tensile stiffness, and interface shear strength. Particle shapes were considered during sand calibration. The scaled pull-out resistance was found to match that of the experimental data. Contributions of the sectional interface shear force to the total pull-out resistance were calculated to explain the progressive failure mechanism mobilised at the tyre-sand interface. The shear force along the tyre strip was not uniformly distributed but higher in the middle portion of the tyre strip. It gradually extended towards the front end of the tyre strip before global interface slipping failure occurred. Comparing the pull-out behaviour of extensible and inextensible tyre strips, the elastic deformation of the tyre strip delayed the occurrence but not the magnitude of peak pull-out force. Micro-mechanical interactions between tyre strip and sand during shear mobilisation were discussed, and induced anisotropy was revealed. The experimental and DEM investigation results in this study provide researchers with an improved understanding of tyre-soil interaction under pull-out loads.

Auto-tuning deep forest for shear stiffness prediction of headed stud connectors

The shear stiffness of headed stud connector is a critical parameter for the calculation of deflection and interfacial shear force for steel–concrete composite structure. Thus, this study presented a promising data-driven model auto-tuning Deep Forest (ATDF) to precisely predict the stud shear stiffness, where the novel Deep Forest algorithm is integrated with the Sequential Model-Based Optimization method to achieve automatic hyperparameter optimization. Six variables having causal relationships with shear stiffness were extracted via mechanism and model analysis, including the effect of weld collar that cannot be considered in existing models and subsequently constituting a database of 425 push-out tests. Then the ATDF model was trained by combining the advantages of deep learning, ensemble learning, and auto-tuning techniques. It was approved to significantly outperform representative benchmark models with R values of 0.91 and 0.87 for training and testing sets. The ATDF was subjected to attribute importance analysis, which quantified the stud diameter and concrete elastic modulus as the most significant variables for shear stiffness, with the stud elastic modulus having the minimal effect. The model uncertainty of ATDF was further evaluated, revealing that it had the lowest bias and variability than those in existing empirical or semi-empirical models. Finally, the reliability analysis was conducted and the partial factors of ATDF under specified target reliability were derived.

Coupling Supramolecular Assemblies and Reactive Oxygen Species (ROS) with Megasonic Action for Applications in Shallow Trench Isolation (STI) Post-Chemical Mechanical Planarization (p-CMP) Cleaning.

Due to the continued miniaturization of semiconductor devices, slurry formulations utilized in the chemical mechanical planarization (CMP) process have become increasingly complex to meet stringent manufacturing specifications. Traditionally, in shallow trench isolation (STI), CMP, a contact cleaning method involving a poly(vinyl alcohol) (PVA) brush, is used to effectively transfer cleaning chemistry to the oxide substrate. This PVA brush can cause nonuniform cleaning chemistry transport, increased interfacial shear force, and cleaning-induced defectivity from brush loading. Previous work with traditional cleaning processes has shown that using “soft” supramolecular cleaning chemistries has dramatically improved cleaning efficacy while also minimizing the number of induced p-CMP defects. To minimize these effects, noncontact cleaning via the implementation of megasonic action has gained attention. This work employs “soft” cleaning chemistries with Cu2+–amino acid complexes, which can catalyze the formation of critical reactive oxygen species (ROS), and evaluates the p-CMP performance under megasonic action. Results from a second-order kinetic model indicate that megasonic conditions (i.e., time and power), “soft” cleaning chemistry structure (i.e., shape and charge), and the generation of ROS all play a critical role in cleaning efficacy under low shear stress conditions.

Interfacial peeling loads in the TBC with an air hole: Analytical solutions and viscoplasticity modelling

This work evaluates the temperature field, stresses, and peeling loads in thermal barrier coatings (TBCs) with air holes subjected to cyclic thermo-mechanical loads during a complete flight. Analytical formulae for the steady-state temperature field and interfacial peeling loads are developed considering thermal gradients in the thickness and longitudinal directions. In addition, viscoplasticity finite element modelling is conducted for the mechanical behaviors of the TBC system. A unified Chaboche-Lemaitre constitutive model that combines a power flow rule with non-linear anisothermal evolution of isotropic and kinematic hardening is integrated into the numerical framework. The results show tensile peeling stress and shear stress are generated in the vicinity of the hole, which motivates the initiation and propagation of hole-edge cracks. The maximum peeling and shear stresses locate close to the thermally grown oxide/bond coat interface and they increase with increasing hole radius. The interfacial peeling moment and shear force could characterize edge cracking in TBCs. As the hole radius increases, the interfacial peeling moment and shear force increase quickly when the hole radius is less than 1 mm but remain stable when the hole radius is beyond 2 mm. This work not only helps to explain the failure mechanisms of hole-edge delamination and spallation in TBCs but also guides the design of thermal barrier coated hot-section components in gas turbines.

New type of shear connector for square concrete-filled tubular columns

Concrete-filled tubes (CFT) are economical and easy to fabricate. As the cross-sections of CFTs are small, the interface shear between steel tube and concrete can be transferred by direct bond. As the cross-sectional dimension increases, shear connectors may be required to transfer the interface shear. However, welding shear connectors inside the steel tube is difficult. In this study, a new type of shear connector that could be installed from outside the steel tube was developed. A pilot test on five specimens demonstrated that the corner shear connector, which is a steel plate located at the corner of a square steel tube, at a 45° angle to the tube wall, is much superior to shear studs in terms of transferring the interfacial shear force. Furthermore, push-out tests of 18 CFT specimens were performed to investigate the strength and the behavior of the corner shear connectors. The strength of the specimens is found to be independent of the cross-sectional area of the shear connector. Instead, the jointed bearing area, which is defined as the cross-sectional area of the shear connection combining the area enclosed by the shear connector and the steel tube, is the major parameter that is closely correlated with the strength of the specimens. Furthermore, the ultimate strength of the specimens is positively correlated with the bearing distance, which is the distance between the loading point and the bearing surface of the connector. In addition, the strength of the corner shear connectors, which have a total jointed bearing area equaling 10.8% of the total concrete area in the steel tube, can adequately satisfy the strictest requirement for the shear transfer.

Modeling of droplet diameter changes during reflood into RELAP5/Mod3.3

Water droplets are generated in the reflood period of a large break loss-of-coolant accident by either shattering of liquid ligament or interfacial shear force. As generated droplets experience vaporization, collision and merging with other droplets, and further breaking up by spacer grid and aerodynamic force, their diameters could vary. Droplet diameter plays an important role in estimating reflood heat and mass transfer, especially in dispersed flow film boiling regime. System thermal-hydraulic analysis code like RELAP5 in which Sauter mean diameter is used as an average diameter in general, however, does not consider mechanistic variation of the diameter. The average diameter is often adjusted as a function of local Weber number in some situations. In this paper, mechanism of droplet size variation and how to accordingly determine Sauter mean diameter are proposed assuming log-normal distribution. And it is validated against RBHT data using RELAP5/Mod3.3 patch 5 code. Proposed model was found to quite well predict Sauter mean diameter of droplets and cladding temperatures of RBHT, especially in droplet-prevailing region. Average difference between measured and calculated cladding temperatures along the core of ten RBHTs was reduced from 42.1 K to 22.1 K with less scatter by 34 K.

Simulation of surface asperities on a carbon fiber using molecular dynamics and fourier series decomposition to predict interfacial shear strength in polymer matrix composites

ABSTRACT The objective of this paper is to predict the fiber/matrix interfacial debond strength in composites. Atomic force microscopy (AFM) images of the surface topography of a de-sized carbon fiber reveal that there are surface asperities present at various length scales ranging from a nanometer to several microns. These asperities are likely caused by shrinkage of the polyacrylonitrile (PAN) precursor during the graphitization process. In order to bridge the length scales, a Fourier series-decomposition covering a range of asperity wavelengths and amplitudes is necessary to effectively capture the roughness of the fiber surface at different length scales. Further, once a surface asperity profile has been resolved into individual subcomponents using Fourier-decomposition, MD simulations can then be employed to obtain the interfacial shear strength of the subcomponent asperity of a given amplitude and wavelength. Finally, by recombining the peak interfacial shear force obtained from each of these subcomponents into the overall shear force for the fiber surface profile, the length-scale-averaged shear strength can be obtained for any given asperity. The objective of this paper is to use this novel approach to determine the interfacial shear strength of de-sized carbon fiber embedded in an epoxy matrix and compare predicted results with experimental data.