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Deformation and stress fields in a curved beam can be tailored by changing its mechanical properties such as the elastic modulus/mass density, which is typically done using functionally graded materials (FGM). Such functional gradation can be done, for instance, by using particles or fiber-reinforced materials with different volume fractions along the beam length. This article presents in-plane vibrations of functionally graded (FG) cantilevered curved beams. Both semi-analytical and finite element modeling are employed to find natural frequencies and mode shapes of such beams. The natural frequencies obtained from the analytical solution and finite element analysis are in close agreement with an error of 6.2% when the variance of material properties gradation is relatively small. In the analytical approach, the direct method is employed to derive the governing linear differential equations of motion. The natural frequencies and mode shapes are obtained using the Galerkin and the finite element methods. First, three natural frequencies and corresponding mode shapes are analyzed for different elastic modulus/mass density distribution functions. Furthermore, the natural frequencies of FG curved beams with a crack are also investigated. Our results indicate that larger cracks near the clamped side of the beam significantly decrease the first natural frequency. In the second and third vibration modes, cracks located in the area with a maximum moment result in the lowest natural frequency values. However, the second and third natural frequencies of the cracked curved beam are not affected by the presence of a crack, if the crack is located at the nodal points of the curved beam.

A new micromechanically motivated theory is proposed to model dragline silk. A thorough review of the micro-structure of dragline silk is presented. Based on the review, a continuum framework is utilized to develop constitutive equation of dragline silk. Dragline silk is composed of a dominant soft amorphous phase ( α -phase) and a reinforcing hard crystal phase, which is classified as rigid β -sheets and extremely soft β -spirals. These two different β -fillers have completely different effects on the mechanical behaviors of dragline silk. The former results in the Mullins effect while the latter produces plastic deformation. Both these effects result in energy dissipation. In addition to these effects, the damping effect due to finite viscoelasticity is accounted for by using a double network model. Moreover, the highly oriented chains in the amorphous phase are modeled as an anisotropic network model. It is found that the proposed model accurately captures the complex mechanical behavior of dragline silk subjected to cyclic loading with merely 7 “physically-based” material constants.

Inflatable structures are commonly used in a variety of engineering applications such as robotics, space structures, medical devices, and automotive safety devices. However, inflation in these systems often requires a non-flexible external pressurized fluid source. Integration of the pressurized fluid source and the flexible construct sacrifices some of the main advantages of the soft structures such as overall flexibility of the system, weight, and cost of fabrication. In this paper, we introduce a novel design for self-inflating structure with embedded pressurizing module. The design is based on integrating a flexible dome with a cylinder. The pressure inside the cylinder is controlled by subjecting dome to a cyclic compression, causing air exchange between the dome and the cylinder. The performance of this design is fully validated through finite element simulations using fluid structure interactions as well as experimental investigations. The results show that a higher pressure is achieved by having smaller dome height. In addition to controlling internal pressure of the cylinder, the design can be used to control the stiffness of the flexible structure such as soft robotics through pressurization. An application of this conceptual device such as pressurizing a tire is presented. This device is integrated within a tire and tire rotation as well as load on the tire have been shown to pressurize the tire. The final pressure and time to achieve maximum pressure depend on the load to the axel of the tire and tire rotational speed, respectively.

Biomimetic scales provide a convenient template to tailor the bending stiffness of the underlying slender substrate due to their mutual sliding after engagement. Scale stiffness can therefore directly impact the substrate behavior, opening a potential avenue for substrate stiffness tunability. Here, we have developed a biomimetic beam, which is covered by tunable stiffness scales. Scale tunability is achieved by specially designed plate like scales consisting of layers of low melting point alloy (LMPA) phase change materials fully enclosed inside a soft polymer. These composite scales can transition between stiff and soft states by straddling the temperatures across LMPA melting points thereby drastically altering stiffness. We experimentally analyze the bending behavior of biomimetic beams covered with tunable stiffness scales of two architectures—one with single enclosure of LMPA and one with two enclosures of different melting point LMPAs. These architectures provide a continuous stiffness change of the underlying substrate post engagement, controlled by the operating temperature. We characterize this response using three-point bending experiments at various temperature profiles. Our results demonstrate for the first time, the pronounced and reversible tunability in the bending behavior of biomimetic scale covered beam, which are strongly dependent on the scale material and architecture. Particularly, it is shown that the bending stiffness of the biomimetic scale covered beam can be actively and reversibly tuned by a factor of up to 7. The developed biomimetic beam has applications in soft robotic grippers, smart segmented armors, deployable structures and soft swimming robots.

Capture of a prey by spider orb webs is a dynamic process with energy dissipation. The dynamic response of spider orb webs under prey impact requires a multi-scale modeling by considering the material microstructures and the assembly of spider silks in the macro-scale. To better understand the prey capture process, this paper addresses a multi-scale approach to uncover the underlying energy dissipation mechanisms. Simulation results show that the microstructures of spider dragline silk play a significant role on energy absorption during prey capture. The alteration of the microstructures, material internal friction, and plastic deformation lead to energy dissipation, which is called material damping. In addition to the material damping in the micro-scale modeling, the energy dissipation due to drag force on the prey is also taken into consideration in the macro-scale modeling. The results indicate that aerodynamic drag, i.e., aero-damping, plays a significant role when the prey size is larger than a critical size.

Displacement and stress fields in a functionally graded (FG) fiber-reinforced rotating annular disk with a non-uniform thickness profile, subjected to angular deceleration and a temperature profile were investigated. Unidirectional fibers were considered to be circumferentially distributed within the disk with fiber volume fraction changing radially. The governing equations for displacement, stress, and temperature fields were solved using finite difference method. The results indicated that thermal induced stresses were more dominate than the rotational induced stresses. Disks which were fiber rich at the inner radius, the fibers made negligible difference on the displacement and stress fields when compared to a homogenous disk made from the matrix material. In addition, it was found that the deceleration magnitude had no effect on the radial and hoop stresses, nor the temperature on the developed shear stress. The shear stress was only affected by the disk deceleration. Tsai-Wu failure criterion was applied for decelerating disks to ascertain their failure behavior. The results show that Tsai-Wu failure index is dominated by the thermal stresses.

We constructed a new class of three-dimensional cellular metamaterials by connecting planar structure with anti-chiral topology. This was achieved by introducing a unique node design for connecting planar materials to enable constructing a three-dimensional architecture. This node design is based on linking the circular elements of the anti-chiral topology using oblique load-bearing ligaments. As the planar structure is subjected to loading, the circular elements rotate and the ligaments undergo bending, resulting in out-of-plane deformation of the three-dimensional cellular metamaterials. The node design, and specifically the ligaments' revolution angle govern the behavior of cellular metamaterials. This was demonstrated by designing cellular metamaterials with a wide range of positive and negative Poisson's ratio in the out-of-plane direction. Keywords: Cellular material, Auxetic behavior, Poisson's ratio, Chirality

The venous morphology of a typical plant leaf affects its mechanical and thermal properties. Such a material could be considered as a fiber reinforced composite structure where the veins and the rest of the leaf are considered as two materials having highly contrast mechanical and thermal properties. The variegated venations found in nature is idealized into three principal fibers—the central mid-fiber corresponding to the mid-rib, straight parallel secondary fibers attached to the mid-fiber representing the secondary veins, and then another set of parallel fibers emanating from the secondary fibers mimicking the tertiary veins of a typical leaf. This paper addresses the in-plane thermal conductivity of such a composite by considering such a venous fiber morphology embedded in a matrix material. We have considered two cases, fibers having either higher or lower conductivity respect to the matrix. The tertiary fibers do not interconnect the secondary fibers in our present study. We carry out finite element based computational investigation of the thermal conductivity of these composites under uniaxial thermal gradients and study the effect of different fiber architectures. To this end, we use two broad types of architectures both having similar central main fiber but differing in either having only secondary fibers or additional tertiary fibers. The fiber and matrix volume fractions are kept constant and a comparative parametric study is carried out by varying the inclination of the secondary fibers. We find the heat conductivity in the direction of the main fiber (Y direction) increases significantly as the fiber angle of the secondary increases. Furthermore, for composite with metal fibers, the conductivity in the Y direction is further enhanced when composite is manufactured by having secondary fibers forming a closed cell structure. However, for composite with ceramic fibers, the conductivity of the composite in the Y direction is little affected by having secondary fibers closed. An opposite behavior is observed when considering conductivity of the composite in the X direction. The conductivity of the composite in the X direction is reduced with increase in the angle of the secondary fibers. Higher conductivity in the X direction is achieved for composite with no closed cells for composites with metal fibers. The results also indicate that for composites with the constant fiber volume fraction, morphology of tertiary fibers may not significantly alter material conductivities. In conclusion, introducing a leaf-mimicking topology in fiber architecture can provide significant additional degrees of tunability in design of these composite structures.

Background Intercondylar notch impingement is detrimental to the anterior cruciate ligament (ACL). Notchplasty is a preventative remodeling procedure performed on the intercondylar notch during ACL reconstruction (ACLR). This study investigates how ACL graft geometry and both tibial and femoral insertion site location may affect ACL-intercondylar notch interactions post ACLR. A range of ACL graft sizes are reported during ACLR, from six millimeters to 11 mm in diameter. Variability of three millimeters in ACL insertion site location is reported during ACLR. This study aims to determine the post-operative effects of minor variations in graft size and insertion location on intercondylar notch impingement. Methods Several 3D finite element knee joint models were constructed using three ACL graft sizes and polar arrays of tibial and femoral insertion locations. Each model was subjected to flexion, tibial external rotation, and valgus motion. Impingement force and contact area between the ACL and intercondylar notch compared well with experimental cadaver data from literature. Results A three millimeter anterior-lateral tibial insertion site shift of the maximum size ACL increased impingement force by 242.9%. A three millimeter anterior-proximal femoral insertion site shift of the maximum size ACL increased impingement by 346.2%. Simulated notchplasty of five millimeters eliminated all impingement for the simulation with the greatest impingement. For the kinematics applied, small differences in graft size and insertion site location led to large increases in impingement force and contact area. Conclusions Minor surgical variations may increase ACL impingement. The results indicate that notchplasty reduces impingement during ACLR. Notchplasty may help to improve ACLR success rates. This report was made possible by an NPRP award [NPRP 5-086-2-031 ] from the Qatar National Research Fund (a member of The Qatar Foundation). Scopus

A typical plant leaf can be idealized as a composite having three principal fibers: the central mid-fiber corresponding to the mid-rib, straight parallel secondary fibers attached to the mid-fiber representing the secondary veins, and then another set of parallel fibers emanating from the secondary fibers mimicking the tertiary fibers embedded in a matrix material. This paper introduces a biomimetic composite design inspired by the morphology of venous leafs and investigates the effects of venation morphologies on the in-plane mechanical properties of the biomimetic composites using finite element method. The mechanical properties such as Young’s moduli, Poisson’s ratio, and yield stress under uniaxial loading of the resultant composite structures was studied and the effect of different fiber architectures on these properties was investigated. To this end, two broad types of architectures were used both having similar central main fiber but differing in either having only secondary fibers or additional tertiary fibers. The fiber and matrix volume fractions were kept constant and a comparative parametric study was carried out by varying the inclination of the secondary fibers. The results show that the elastic modulus of composite in the direction of main fiber increases linearly with increasing the angle of the secondary fibers. Furthermore, the elastic modulus is enhanced if the secondary fibers are closed, which mimics composites with closed cellular fibers. In contrast, the elastic modulus of composites normal to the main fiber ( x direction) exponentially decreases with the increase of the angle of the secondary fibers and it is little affected by having secondary fibers closed. Similar results were obtained for the yield stress of the composites. The results also indicate that Poisson’s ratio linearly increases with the secondary fiber angle. The results also show that for a constant fiber volume fraction, addition of various tertiary fibers may not significantly enhance the mechanical properties of the composites. The mechanical properties of the composites are mainly dominated by the secondary fibers. Finally, a simple model was proposed to predict these behaviors.

Conventional single-lap adhesive joints between identical adherends achieve ultimate strength only after significant inelastic deformation of the adhesive and perhaps also the adherends. However purely elastic analysis provides insights and is relevant to fatigue initiation or brittle failure. We extend classical beam-based elastic results, both ‘within the bond’ (deriving more-accurate peak peel stress from the joint-edge moment) and ‘beyond the bond’ (determining the edge moment from adherend dimensions, remote boundary conditions, and load). Within the bond, we show that peak adhesive equivalent stress and principal stress are minimized when the bond length exceeds four characteristic lengths of the elastic-foundation shear stress equation. This makes simplified ‘long’ joint formulas attractive for initial design. We then examine how well the long-joint predicted peak peel stress matches plane strain finite element analysis, and empirically capture a peel-stress end effect due to nonzero adhesive Poisson ratio. With this end-effect correction, the limit of useful accuracy can be expressed as a ratio R a of (adherend axial stiffness) to (adhesive axial stiffness) being > a number of order 10 2 - 10 3 depending on Poisson ratio. This limit supplements the Goland and Reissner proposed applicability limit for elastic foundation analysis, expressed as a limiting ratio R v of through-thickness or vertical stiffnesses. Outside the bond, Timoshenko-style beam-column expressions are used to derive a simplified joint-edge moment factor. While similar in spirit to the edge-moment determination of Goland and Reissner for infinite-length pinned adherends, treating the bond region as a rigid block leads to simpler nonlinear expressions, and captures the moment-reducing benefits of shorter (finite-length) adherends and fixed-slope end conditions. Joint rotation effects become dominant when T L 2 > E I ( L is adherend free length, T is tensile load), then joint rotation magnitude depends on T D 2 / E I ( D is lap length).

Structural response and failure modes of honeycomb sandwich panels subjected to a shock (impulsive pressure) followed by a high velocity projectile impact were investigated using detailed finite element simulations. Performance of sandwich panels was quantified by maximum transverse deflection of the bottom face sheet and core crushing strain along with an investigation of their optimal behavior. Three failure modes were observed in panels - core failure, top face failure, and tearing and detachment from support. Failure maps of honeycomb sandwich panels were constructed to show the failure mode of panels as a function of shock intensity, projectile velocity and panel core relative density. In addition, a limited set of simulations were carried out to study the role of incident angle of projectile on the overall performance of a panel. These simulations showed that maximum deflection occurred for vertically impacting projectiles. However, we found that this did not directly translate to maximum core crushing strain in sandwich panels. The results provide new insight into the performance and failure of sandwich panels under complex dynamic loading conditions, and further highlight the potential of these panels for development of threat-resistant structural systems. 2016 Elsevier Ltd. All rights reserved. This work has been supported by the Qatar National Research Fund (QNRF) under Award Number NPRP 5-1298-2-560 . The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the Qatar National Research Fund. Scopus

Out of plane vibration of rotating disks limits their performances especially at certain critical speed. The critical speed of these disks may be affected by the presence of defects such as a circumferential crack. In this paper out of plane vibration of functionally graded (FG) rotating annular disks with a circumferential open crack is investigated. The cracked disk is modeled as two sub-disks, connected at the crack location by translational and rotational line springs, simulating the crack plate response to induced shear force and bending moment at the crack radius. These spring stiffness constants are obtained numerically using the finite element method (FEM) as a function of crack depth and radius. The rotational spring stiffness strongly depends on the disk rotation speed, while the stiffness of the translational spring is found to be independent of the disk speed. Both spring constants depend on the spatial distribution of the disk elastic modulus. The in-plane disk stresses are obtained using a semi-analytical approach. Those in plane stresses are used to obtain the governing equation of out of plane motion of the disk. A finite difference scheme is used to solve the partial differential equation of motion to obtain eigenvalues, critical speed and associated mode shapes. The lowest critical speed, which is one of the important parameters limiting the performance of the rotating disk, is obtained from the Campbell Diagram. It is found that irrespective of the distribution of the modulus of elasticity in the FG disk, increasing the crack depth or decreasing the crack radial distance from the disk center decreases the critical speed. The critical speed reduction is more pronounced for the case when the disk material modulus of elasticity is decreasing from the disk center. 2016 Elsevier Ltd. All rights reserved. This work has been supported by the Qatar National Research Foundation (QNRF) under Award no. NPRP 5-068-2-024 . Scopus

This paper highlights the effects of cell wall material strain hardening and density functional gradation (FG) on in-plane constant-velocity dynamic crushing response and impact behavior of hexagonal honeycombs. Results show that cell wall material strain hardening influences the distinct deformation modes induced by crushing velocity generally observed in regular hexagonal honeycombs. This is seen by a delay in the onset of localized deformation up until intermediate crushing velocities after which localization becomes dominant smearing out differences brought about by cell wall material strain hardening (plasticity convergence). In addition, during the impact loading on regular honeycombs, it was found that increasing the cell wall material strain hardening decreases the rate of gain of maximum crushing strain with increments in initial kinetic energy of impact. On the other hand, introducing FG brings about new deformation patterns due to changes in material distribution and preferential cell wall collapse of the weaker members. Interestingly, although the dynamic localization effect at higher crushing velocities observed earlier was not found to be particularly affected by FG, gradient convergence (i.e. smearing out the effects of FG due to higher velocities analogous to plasticity convergence) was not observed. On the contrary, gradient convergence emerged at higher impacting velocities primarily brought about by a combination of initial deformation localization and its subsequent advancement into FG region ahead. The kinetic energy threshold for the emergence of this gradient convergence effect was found to be considerably delayed by cell wall material strain hardening.

Displacement and stress fields in a functionally graded (FG) fiber-reinforced rotating disk of nonuniform thickness subjected to angular deceleration are obtained. The disk has a central hole, which is assumed to be mounted on a rotating shaft. Unidirectional fibers are considered to be circumferentially distributed within the disk with a variable volume fraction along the radius. The governing equations for displacement and stress fields are derived and solved using finite difference method. The results show that for disks with fiber rich at the outer radius, the displacement field is lower in radial direction but higher in circumferential direction compared to the disk with the fiber rich at the inner radius. The circumferential stress value at the outer radius is substantially higher for disk with fiber rich at the outer radius compared to the disk with the fiber rich at the inner radius. It is also observed a considerable amount of compressive stress developed in the radial direction in a region close to the outer radius. These compressive stresses may prevent any crack growth in the circumferential direction of such disks. For disks with fiber rich at the inner radius, the presence of fibers results in minimal changes in the displacement and stress fields when compared to a homogenous disk made from the matrix material. In addition, we concluded that disk deceleration has no effect on the radial and hoop stresses. However, deceleration will affect the shear stress. Tsai–Wu failure criterion is evaluated for decelerating disks. For disks with fiber rich at the inner radius, the failure is initiated between inner and outer radii. However, for disks with fiber rich at the outer radius, the failure location depends on the fiber distribution.

Anisotropic hierarchical honeycombs of uniform wall-thickness are constructed by repeatedly replacing each three-edge vertex of a base hexagonal network with a similar but smaller hexagon of the same orientation, and stretching the resulting structure in horizontal or vertical directions to break the isotropy. The uniform overall thickness is then adjusted to maintain the constant average density. The resulting fractal-appearing hierarchical structure is defined by the ratios of replacement edge lengths to the underlying network edge length and also the cell wall angle. The effective elastic modulus, Poisson׳s ratio and plastic collapse strength in the principal directions of hierarchical honeycombs were obtained analytically as well as by finite element analyses. The results show that anisotropic hierarchical honeycombs of first to fourth order can be 2.0–8.0 times stiffer and at the same time up to 2.0 times stronger than regular honeycomb at the same wall angle and the same overall average density. Plastic collapse analysis showed that anisotropic hierarchical honeycomb has the larger plastic collapse strength compared to regular hierarchical honeycomb of the same order at certain oblique wall angles. The current work provides insight into how incorporating anisotropy into the structural organization can play a significant role in improving the mechanics of the materials structure such as regular or hierarchical honeycombs, and introduces new opportunities for development of novel materials and structures with desirable and actively tailorable properties.

Tri-leaflet polyurethane heart valves have been considered as a potential candidate in heart valve replacement surgeries. In this study, polyurethane (Angioflex(®)) heart valve prostheses were fabricated using a solvent-casting method to evaluate their calcification resistance. These valves were subjected to accelerated life testing (continuous opening and closing of the leaflets) in a synthetic calcification solution. Results showed that Angioflex(®) could be considered as a potential material for fabricating prosthetic heart valves with possibly a higher calcification resistance compared to tissue valves. In addition, calcification resistance of bisphosphonate-modified Angioflex(®) valves was also evaluated. Bisphosphonates are considered to enhance the calcification resistance of polymers once covalently bonded to the bulk of the material. However, our in-vitro results showed that bisphosphonate-modified Angioflex(®) valves did not improve the calcification resistance of Angioflex(®) compared to its untreated counterparts. The results also showed that cyclic loading of the valves' leaflets resulted in formation of numerous cracks on the calcified surface, which were not present when calcification study did not involve mechanical loading. Further study of these cracks did not result in enough evidence to conclude whether these cracks have penetrated to the polymeric surface.

Stress field in functionally graded (FG) rotating disks with non-uniform thickness and variable angular velocity is studied numerically. The elastic modulus and mass density of the disks are assumed to be varying along the radius as a power-law function of the radial coordinate, while the Poisson's ratio is kept constant. The governing equations for the stress field is derived and numerically solved using the finite difference method for the case of fixed-free boundary conditions. Additionally, the effect of material gradient index (i.e., the level of material gradation) on the stress field is evaluated. Our results show that the optimum stress field is achieved by having a thickness profile in the form of a rational function of the radial coordinate. Moreover, a smaller stress field can be developed by having greater mass density and elastic modulus at the outer radius of the disk (i.e., ceramic-rich composites at the outer radius). The numerical results additionally reveal that deceleration results in shear-stress development within the disks where a greater deceleration leads to greater shear stress; however this has almost no effect on the radial and circumferential stresses. Furthermore, the shear stress can cause a shift in the location of the maximum Von Mises stress, where for small deceleration, maximum Von Mises stress is located somewhere between the inner and outer radii, while for large deceleration it is located at the inner radius. This report was made possible by a NPRP award [NPRP 5–068-2–024] from the Qatar National Research Fund (a member of the Qatar Foundation).

We demonstrated the feasibility of harvesting mechanical energy through the proper design and installation of a lattice structure which undergoes snap-through deformation under applied mechanical loading. First, the theoretical formulations for both symmetric and asymmetric modes of the snap-through deformation in a 2D lattice structure were derived. Then, experiments were conducted on the prototype to measure the energy harvesting ability at different frequencies and to investigate the capability of charging a capacitor connected to the lattice prototype. Finally, the effects of the defect in the lattice on energy harvesting were discussed. Our results showed that the average generated voltage across a 25 kΩ resistor increased by increasing the frequency of loading. However, energy stored in a capacitor was independent of loading frequency. For a defective structure with a fixed vertex, the generated voltage is lower yet increasing with the frequency of loading. The designed structure is robust and provides sustainable energy output under cyclic loading even with the presence of defects and imperfections.We demonstrated the feasibility of harvesting mechanical energy through the proper design and installation of a lattice structure which undergoes snap-through deformation under applied mechanical loading. First, the theoretical formulations for both symmetric and asymmetric modes of the snap-through deformation in a 2D lattice structure were derived. Then, experiments were conducted on the prototype to measure the energy harvesting ability at different frequencies and to investigate the capability of charging a capacitor connected to the lattice prototype. Finally, the effects of the defect in the lattice on energy harvesting were discussed. Our results showed that the average generated voltage across a 25 kΩ resistor increased by increasing the frequency of loading. However, energy stored in a capacitor was independent of loading frequency. For a defective structure with a fixed vertex, the generated voltage is lower yet increasing with the frequency of loading. The designed structure is robust and provi...

This study determined which knee joint motions lead to anterior cruciate ligament (ACL) rupture with the knee at 25° of flexion. The knee was subjected to internal and external rotations, as well as varus and valgus motions. A failure locus representing the relationship between these motions and ACL rupture was established using finite element simulations. This study also considered possible concomitant injuries to the tibial articular cartilage prior to ACL injury. The posterolateral bundle of the ACL demonstrated higher rupture susceptibility than the anteromedial bundle. The average varus angular displacement required for ACL failure was 46.6% lower compared to the average valgus angular displacement. Femoral external rotation decreased the frontal plane angle required for ACL failure by 27.5% compared to internal rotation. Tibial articular cartilage damage initiated prior to ACL failure in all valgus simulations. The results from this investigation agreed well with other experimental and analytical investigations. This study provides a greater understanding of the various knee joint motion combinations leading to ACL injury and articular cartilage damage. Scopus

Anterior cruciate ligament (ACL) disruption is a common injury that is detrimental to an athlete's quality of life. Determining the mechanisms that cause ACL injury is important in order to develop proper interventions. A failure locus defined as various combinations of loadings and movements, internal/external rotation of femur and valgus and varus moments at a 25(o) knee flexion angle leading to ACL failure was obtained. The results indicated that varus and valgus movements were more dominant to the ACL injury than femoral rotation. Also, Von Mises stress in the lateral tibial cartilage during the valgus ACL injury mechanism was 83% greater than that of the medial cartilage during the varus mechanism of ACL injury. The results of this study could be used to develop training programmes focused on the avoidance of the described combination of movements which may lead to ACL injury.

The process of adaptive bone remodeling can be simulated with a self-optimizing finite element method. The basic remodeling rules attempt to obtain a constant value for the strain energy per unit bone mass, by adapting density. The precise solution is dependent on the loads, initial conditions, and the parameters of the remodeling rule. While there are several investigations on developing algorithms leading to the bone density distribution in the proximal femur, these algorithms often require a large number of iterations. The aim of this study was to develop a more efficient adaptive bone remodeling algorithm, and to identify how the bone density distribution of the proximal femur was affected by parameters that govern the remodeling process. The forces at different phases of the gait cycle were applied as boundary conditions. The bone density distributions from these forces were averaged to estimate the density distribution in the proximal femur. The effect of varying the initial bone density, spatial influence function, non-linear order of the adaptive algorithm, and the influence range on the converged solution were investigated. The proposed procedure was shown to converge in a fewer number of iterations and requiring less computational time, while still generating a realistic bone density distribution. It was also shown that varying the identified parameters within reasonable upper and lower bounds had very little impact on the qualitative form of the converged solution. In contrast, the convergence rate was affected to a greater degree by variation of these parameters. In all cases, the solutions obtained are comparable with the actual density in the proximal femur, as measured by Dual-energy X-ray absorptiometry (DEXA) scans.

A series of analytical relationships is presented to predict the mechanical properties and response of open three-dimensional Voronoi tessellation of face-centered cubic structures called rhombic dodecahedrons. The cell edge material was assumed to be elastic–perfectly plastic, and the effective mechanical properties of the cellular structure were related to the cell edge material properties and the relative density of the cellular structure. Detailed finite element models were carried out to establish the validity of the analytical models. In the elastic regime, the monodisperse cellular structure is orthotropic and near-incompressible in all loading directions, and its response is governed by bending deformation of the cell edges. The yield strength of the cellular structure in all loading directions is equal. We also studied the role of irregularity in the organization of the cellular structure on its mechanical properties. The irregularity in the cellular structure organization was introduced by moving the vertices of a regular cellular structure in three orthogonal directions by a random value within a predefined range called the “irregularity index”. At a constant overall relative density, increasing the level of irregularity increases the effective elastic modulus and significantly decreases the effective yield strength of the cellular structure. We also studied the mechanical properties of the cellular structure tied to rigid plates, in view of the application of cellular structure as the core construction of sandwich panels. In this case, the cellular structure is significantly stiffer and its mechanical response is dominated by cell wall stretching.

A series of experiments and detailed finite element simulations were carried out to study the performance of single lap joints with non-flat interfaces loaded at a small angle to the mean bond plane. In the experimental part, fiber reinforced epoxy composite adherends with sinusoidal bonding surfaces (but no change to the exterior sample dimensions) were fabricated in a purpose-built mold. This construction method allowed the fibers to follow the sinusoidal profile for maximum strength. Then the sinusoidal surfaces were joined by a controlled-thickness layer of epoxy. Single lap joints with a flat interface were also fabricated using the same composite material and with the same overall shape. The experiments showed that the interface non-flatness has significant effect on the mechanical behavior and strength of the bonded joints. Finite element simulations of a simplified two-dimensional model with isotropic adherends were also carried out to estimate the distribution of shear and peeling stresses along the bonded joints, and the results were related to the experimental observations. Parametric variations were studied via FEA to highlight the role of interface shape, adhesive elastic modulus and a central void size on the distribution of stresses, and inherently the overall strength and behavior of the bonded joints.

A simple and effective in situ method for strengthening or healing thin-wall structures is presented. In this method, a liquid-state gap-sealing foam is injected within the enclosed spaces of a structure. After injection it expands to fill and pressurize the cavities, then solidifies in few hours. The stiff pressurized foam enhances load carrying capacity both by supporting part of the load, and by retarding the buckling of thin-wall structural components. A simple demonstration of the proposed technique is provided by load-testing thin-wall beverage cans, and also both intact and damaged aluminum honeycomb, filled with commercially available gap-sealing polyurethane foam. By adding foam, the structures' peak load and energy absorption were significantly enhanced. The injected foam partially restored the original undeformed shape during unloading, highlighting the potential advantage to apply this method for multiple-use energy absorbing components. Qatar National Research Foundation (QNRF) Award Number NPRP 09-145-2-061 Scopus

Wood plastic composite (WPC) specimens were fabricated in shapes relevant to flute (musical instrument) production using African blackwood powder and phenolic resin in a hot compression molding setup. The roles of composition and processing parameters on the mechanical properties (flexural strength, elastic modulus, and impact failure energy) were systematically investigated. Cracks were observed in composites with more than 70% wood particles due to the formation of gas in the system during manufacturing, and lack of fluidity in the system to flush out entrapped air and the produced gases. Based on these results, the optimum temperature, pressure, and wood volume fraction for manufacturing WPC in the form of a flute is developed. A further series of experimental procedures were performed to improve the mechanical properties of WPC samples by studying the addition of short glass fibers to the molding compound prior to hot pressing. The results showed that the addition of short fiber did not improve the strength of WPC but rather reduced its strength compared to unreinforced composite. This was attributed to lack of bonding between the short fibers and composite matrix.

The in-plane dynamic crushing of two dimensional honeycombs with both regular hexagonal and irregular arrangements was investigated using detailed finite element models. The energy absorption of honeycombs made of a linear elastic-perfectly plastic material with constant and functionally graded density were estimated up to large crushing strains. Our numerical simulations showed three distinct crushing modes for honeycombs with a constant relative density: quasi-static, transition and dynamic. Moreover, irregular cellular structures showed to have energy absorption similar to their counterpart regular honeycombs of same relative density and mass. To study the dynamic crushing of functionally graded cellular structures, a density gradient in the direction of crushing was introduced in the computational models by a gradual change of the cell wall thickness. Decreasing the relative density in the direction of crushing was shown to enhance the energy absorption of honeycombs at early stages of crushing. The study provides new insight into the behavior of engineered and biological cellular materials, and could be used to develop novel energy absorbent structures.

Subject-specific models were developed and finite element analysis was performed to observe the effect of the frontal plane tibiofemoral angle on the normal stress, Tresca shear stress and normal strain at the surface of the knee cartilage. Finite element models were created for three subjects with different tibiofemoral angle and physiological loading conditions were defined from motion analysis and muscle force mathematical models to simulate static single-leg stance. The results showed that the greatest magnitude of the normal stress, Tresca shear stress and normal strain at the medial compartment was for the varus aligned individual. Considering the lateral knee compartment, the individual with valgus alignment had the largest stress and strain at the cartilage. The present investigation is the first known attempt to analyze the effects of tibiofemoral alignment during single-leg support on the contact variables of the cartilage at the knee joint. The method could be potentially used to help identify individuals most susceptible to osteoarthritis and to prescribe preventive measures.

The residual compressive stresses induced by the autofrettage process in a metal vessel are limited by metal plasticity. Here we showed that the autofrettage of layered metal–ceramic composite vessels leads to considerably higher residual compressive stresses compared to the counterpart metal vessel. To calculate the residual stresses in a composite vessel, an extension of the Variable Material Properties (X-VMP) method for materials with varying elastic and plastic properties was employed. We also investigated the autofrettage of composite vessels made of functionally graded material (FGM). The significant advantage of this configuration is in avoiding the negative effects of abrupt changes in material properties in a layered vessel – and thus, inherently, in the stress and strain distributions induced by the autofrettage process. A parametric study was carried out to obtain near-optimized distribution of ceramic particles through the vessel thickness that results in maximum residual stresses in an autofrettaged functionally graded composite vessel. Selected finite element results were also presented to establish the validity of the X-VMP method.

Subject-specific three-dimensional finite element models of the knee joint were created and used to study the effect of the frontal plane tibiofemoral angle on the stress and strain distribution in the knee cartilage during the stance phase of the gait cycle. Knee models of three subjects with different tibiofemoral angle and body weight were created based on magnetic resonance imaging of the knee. Loading and boundary conditions were determined from motion analysis and force platform data, in conjunction with the muscle-force reduction method. During the stance phase of walking, all subjects exhibited a valgus-varus-valgus knee moment pattern with the maximum compressive load and varus knee moment occurring at approximately 25% of the stance phase of the gait cycle. Our results demonstrated that the subject with varus alignment had the largest stresses at the medial compartment of the knee compared to the subjects with normal alignment and valgus alignment, suggesting that this subject might be most susceptible to developing medial compartment osteoarthritis (OA). In addition, the magnitude of stress and strain on the lateral cartilage of the subject with valgus alignment were found to be larger compared to subjects with normal alignment and varus alignment, suggesting that this subject might be most susceptible to developing lateral compartment knee OA.

A 3D finite element model of rib cage movement is developed and used to study the role of age-related costal cartilage and sternocostal joint calcification, as well as respiratory muscle weakness on the 'bucket-handle' movement of human rib. The volume displacement of the rib cage is related to changes in its circumference using an empirical equation presented by Agostoni et al. (1965, J Appl Physiol, 20:1179-1186). A systematic study is carried out to quantify the role of costal cartilage, sternocostal joint calcification and muscle weakness on the volume displacement of the rib cage. The results provide insight into some of the mechanisms underlying age-related changes in the respiratory system.

We used an extension of the Variable Material Property method for materials with varying elastic and plastic properties to evaluate the residual stresses in an autofrettaged thick vessel made of functionally graded metal–ceramic composite. It is shown that the reinforcement of the metal vessel by ceramic particles, with an increasing ceramic volume fraction from inner to outer radius, increases the magnitude of compressive residual stresses at the inner section of an autofrettaged vessel and thus, could lead to better fatigue life and load-carrying capacity of the vessel. A parametric study is carried out to highlight the role of ceramic particle strength and spatial distribution, as well as the autofrettage pressure on the induced residual stresses in a thick vessel.

Functionally graded cellular structures such as bio-inspired functionally graded materials for manufacturing implants or bone replacement, are a class of materials with low densities and novel physical, mechanical, thermal, electrical and acoustic properties. A gradual increase in cell size distribution, can impart many improved properties which may not be achieved by having a uniform cellular structure. The material properties of functionally graded cellular structures as a function of density gradient have not been previously addressed within the literature. In this study, the finite element method is used to investigate the compressive uniaxial and biaxial behavior of functionally graded Voronoi structures. Furthermore, the effect of missing cell walls on its overall mechanical (elastic, plastic, and creep) properties is investigated. The finite element analysis showed that the overall effective elastic modulus and yield strength of structures increased by increasing the density gradient. However, the overall elastic modulus of functionally graded structures was more sensitive to density gradient than the overall yield strength. The study also showed that the functionally graded structures with different density gradient had similar sensitivity to random missing cell walls. Creep analysis suggested that the structures with higher density gradient had lower steady-state creep rate compared to that of structures with lower density gradient.

Cellular solids such as foams are widely used in engineering applications. In these applications, it is important to know their mechanical properties and the variation of these properties with the presence of defects. Several models have been proposed to obtain the mechanical properties of cellular materials. However, these models are usually based on idealized unit cell structures, and are not suitable for finding the mechanical properties of cellular materials with defects. The objective of this work is to understand the effect of missing walls and filled cells on elastic–plastic behavior of both regular hexagonal and non-periodic Voronoi structures using finite element analysis. The results show that the missing walls have a significant effect on overall elastic properties of the cellular structure. For both regular hexagonal and Voronoi materials, the yield strength of the cellular structure decreases by more than 60% by introducing 10% missing walls. In contrast, the results indicate that filled cells have much less effect on the mechanical properties of both regular hexagonal and Voronoi materials. The effects of material strain hardening on the yield strength of cellular materials are also investigated.

Studying the mechanics of the knee joint has direct implications in understanding the state of human health and disease and can aid in treatment of injuries. In this work, we developed an axisymmetric model of the human knee joint using finite element method, which consisted of separate parts representing tibia, meniscus and femoral, and tibial articular cartilages. The articular cartilages were modeled as three separate layers with different material characteristics: top superficial layer, middle layer, and calcified layer. The biphasic characteristic of both meniscus and cartilage layers were included in the computational model. The developed model was employed to investigate several aspects of mechanical response of the knee joint under external loading associated with the standing posture. Specifically, we studied the role of the material characteristic of the articular cartilage and meniscus on the distribution of the shear stresses in the healthy knee joint and the knee joint after meniscectomy. We further employed the proposed computational model to study the mechanics of the knee joint with an artificial meniscus. Our calculations suggested an optimal elastic modulus of about 110 MPa for the artificial meniscus which was modeled as a linear isotropic material. The suggested optimum stiffness of the artificial meniscus corresponds to the stiffness of the physiological meniscus in the circumferential direction.

Friction and wear behavior of copper matrix composites reinforced by unidirectional Nb fibers were explored using both pin-on-ring and pin on disk set-ups. Composite specimens were manufactured from a Cu–18 vol.% Nb powder mixture. Through various mechanical processes and heat treatments, this powder mixture was converted to a ‘ribbon-shaped Nb’ fiber reinforced copper composite with final average fiber thickness of about 10 nm and aspect ratio of about 30. The friction and wear properties of this composite were evaluated against gray cast iron with the hardness of 92 HRB. The effects of normal load, sliding speed and fiber orientation on the friction and wear of this composite were investigated. Steady state wear was observed upon formation of a thin film on the wear surface for all the specimens. This film formed due to the material transfer from the disk to the composite surface due to low ductility of the copper matrix. The wear rate was proportional to the sliding distance and normal load for all specimens, while specimens with fibers normal to the sliding surface showed the lowest wear rate. Moreover, the wear rate appeared to be an exponential function of the sliding speed. This was related to temperature rise at the interface of sliding surfaces and recovery of Cu matrix and possible breakage of the Nb fibers. Metalographic examination of Cu–Nb micro-fiber reinforced composite showed that when exposed to temperature greater than 600 °C, fibers start to break and spherodized. This phenomenon significantly reduces the strength of Cu–Nb composite and increases its wear rate. Some insight into the mechanisms of wear was obtained using optical and scanning electron microscopy and energy dispersive spectrometry analysis of the surface.

A non-destructive evaluation method for predicting the residual tensile strength of erosion damaged fiber-reinforced composites was developed based on monitoring the acoustic emission (AE) activity of the composite specimens during uniaxial tensile loading. The developed method was used for estimating the residual strength of E-glass/epoxy composite with ply sequence of [45°/−45°/0°/45°/−45°/0°] S . A mixture of air and SiC particles with diameter of 400–500 μm was blasted to the composite specimens at various impact angles and durations to induce the local damage. Subsequently, uniaxial tensile tests were carried out on the specimens subjected to solid particle erosion as well as undamaged specimens while monitoring the acoustic emission activity. The extent and mechanisms of damage due to tensile loading of composite specimens were explored by examining the failure surface upon completion of tensile tests under a scanning electron microscope (SEM) and by measuring the distribution of AE events by event duration, ring down counts and energy distribution during tensile tests. Weibull probability distribution model and AE stress delay parameter model were developed to relate the AE activity to the erosion damage and residual strength. The results show that the developed non-destructive method is capable of predicting the residual strength of composites subjected to solid particle damage.

The dynamic response of repaired composite beams under a harmonic peeling load was studied theoretically and experimentally. The repair method was based on removal of the damaged region and bonding a composite patch into the gap with adhesive. In the theoretical part, the equations of motion in the axial and transverse directions were derived assuming that the viscoelastic adhesive layer resists both peeling and shear stresses and both the patch and parent materials behave as Euler–Bernouli beams. The validity of the theoretical model for evaluating the dynamic response of repaired composite beams was examined with the results of the finite element model. The finite element results indicated that the deformation mechanism of the repaired composite beam depends on the adhesive elastic modulus. For low values of the adhesive elastic modulus, shear deformation in the adhesive layer is the dominant deformation mechanism and the proposed theoretical model replicated the results of the computational analysis. In the experimental part, the response of unidirectional fiberglass-reinforced epoxy composite specimens with various repaired patch lengths, thickness, and material properties were measured by hammer test technique using a non-contact laser vibrometer. The patch section was either the fiberglass-reinforced epoxy composite or E-glass fiber reinforced composites with various stacking sequences. The repairing patches were bonded to the composite beam with an epoxy. The experimental results were compared to those of the theoretical model and finite element analyses. The experimental results were related to the adhesive material properties, its loss factor and to the patch material properties.

Turbo-generator shafts are often subjected to complex dynamic torsional loadings, resulting in generation and propagation of circumferential cracks. Mode III fatigue crack growth generally results in a fracture surface consisting of peaks and valleys, resembling a factory roof. The fracture surface roughness depends on the material microstructure, the material yield strength, and the applied cyclic torque amplitude. This crack pattern can severely affect the vibration characteristics of the shafts. The accurate evaluation of the torsional dynamic response of the turbo-generator shafts entails considering the local sources of energy loss in the crack vicinity. The two most common sources of the energy loss are the local energy loss due to the plasticity at the crack tip and frictional energy loss due to interaction of mutual crack surfaces. A theoretical procedure for evaluating the values of the system loss factors corresponding to these sources of energy loss is presented. Furthermore, the local flexibility is obtained by evaluating the resistance of the cracked section of the shaft to the rotational displacement. The shaft material is assumed to be elastic perfectly plastic. The effects of the applied Mode III stress intensity factor and the crack surface pattern parameters on the energy loss due to the friction and the energy loss due to the plasticity at the crack tip are investigated. The results show that depending on the amplitude of the applied Mode III stress intensity factor, one of these energy losses may dominate the total energy loss in the circumferentially cracked shaft. The results further indicate that the torsional dynamic response of the turbo-generator shaft is significantly affected by considering these two sources of the local energy loss.

The effect of solid particle erosion on the strength and fatigue properties of E-glass/epoxy composite is investigated. Solid particle erosion with SiC particles of 400–500 μm in diameter is simulated on 12-ply [45°/–45°/0°/45°/–45°/0°]S E-glass/epoxy composites with a constant particle velocity of 42.5 m/s and a solid particle to air volume ratio of 6 kg/m3 at impact angles of 90, 60, and 30° for 30, 60, 90, and 120 s. Damaged and undamaged specimens are subjected to tensile tests while monitoring their acoustic emission (AE) activity. An erosion damage parameter is defined as a function of the particle impact angle and the erosion duration to determine the residual tensile strength of the composite. Scanning electron microscope (SEM) images of the erosion-damaged specimens reveal that the same damage mechanism occurs at different impact angles. The AE stress delay parameter is used to predict the residual tensile strength of erosion-damaged composites. Tension–tension fatigue tests are performed on virgin specimens and specimens exposed to erosion damage of 60 and 90s at 90° particle impact angle to observe the effects of erosion damage on the fatigue life. A modified Basquin's equation is defined to predict the fatigue life of the erosion-damaged specimens.

Summary Objective The main objective of this study was to evaluate the wear characteristics of fiber-reinforced dental composites. Variables under investigation include the fiber weight percent added to the matrix as well as fiber length. Methods Dental specimens with glass fiber content of 2, 5.1, 5.7, and 7.6 wt% with fiber length of either 1.5 or 3 mm, were prepared by mixing an activated dental resin with commercial glass fibers. The specimens were then tested on a pin on disc setup, where the antagonist disc was manufactured of a similar fiber-reinforced composite with 5.1 wt% fiber and fiber length of 3 mm. The volume loss and coefficient of friction of the specimens was monitored periodically throughout testing. In addition, the wear surfaces of all specimens were evaluated using a scanning electron microscope. Results The specimens with 5.7 wt% fibers and fiber length of 3 mm performed better in this study compared to all other fiber-reinforced specimens under all load conditions. In fact, this specimen had a comparable wear rate to a particle-filled dental composite. For the fiber lengths considered, increasing the length of the fibers increased the wear resistance of the specimen. The coefficient of friction showed a good correlation with the wear resistance of specimens. Significance Fiber-reinforced composites demonstrated a high resistance to wear and may therefore be advantageous for dental applications, where high wear resistance is essential to functionality.

In this study, a model of femur which resembles bone natural structure has been developed. The model initially consists of a solid shell representing cortical bone encompassing a cubical network of interconnected rods with circular cross-sections representing trabecular bone part. A computational efficient program has been developed which iteratively changes the structure of trabecular bone by keeping the local stress in the structure within a defined stress range. The stress is controlled by either enhancing existing beam elements or removing beams from the initial trabecular frame structure. Trabecular bone structure is obtained for two load cases: walking and stair climbing. The results show that as the magnitude of the loads increase, the internal structure gets denser in critical zones. The higher density is achieved using loading associated with the stair climbing. Walking which is considered as the routine daily activity, results in the less internal density in different regions of the bone. The results show that the converged bone architecture consisting of rods and plates are consistent with the natural bone morphology of femur. Furthermore, the bone volume fraction at the critical regions of the converged structure is in a good agreement with previously measured data obtained from combinations of Dual X-ray Absorptiometry (DXA) and Computed Tomography (CT).Copyright © 2014 by ASME

Turbine-generator shafts are often subjected to a complex transient torsional loading. Such transient torques may initiate and propagate a circumferential crack in the shafts. Mode III crack growth in turbo-generator shafts often results in a fracture surface morphology resembling a factory roof. The interaction of the mutual fracture surfaces results in a pressure and a frictional stress field between fracture surfaces when the shaft is subjected to torsion. This interaction reduces the effective Mode III stress intensity factor. The effective stress intensity factor in circumferentially cracked round shafts is evaluated for a wide range of applied torsional loading by considering a pressure distribution between mating fracture surfaces. The pressure between fracture surfaces results from climbing of asperities respect to each other. The pressure profile not only depends on the fracture surface roughness (height and width (wavelength) of the peak and valleys), but also depends on the magnitude of the applied Mode III stress intensity factor. The results show that asperity interactions significantly reduce the effective Mode III stress intensity factor. However, the interactions diminish beyond a critical applied Mode III stress intensity factor. The critical stress intensity factor depends on the asperities height and wavelength. The results of these analyses are used to find the effective stress intensity factor in various Mode III fatigue crack growth experiments. The results show that Mode III crack growth rate is related to the effective stress intensity factor in a form of the Paris law.

Dynamic response of single lap joints, subjected to a harmonic peeling load is studied theoretically and experimentally. In the theoretical part, dynamic response of a single lap joint clamped at one end and subjected to a harmonic peeling load at the other end is investigated. Adherents are modeled as Euler-Bernouli beams joined in the lap area by a viscoelastic adhesive layer. Both axial and transverse deformations of adherents are considered in deriving the equations of motion. The effects of adhesive layer thickness, mechanical properties and its loss factor on the dynamic response of the joint are investigated. Furthermore, effects of defects such as a void in the lap area on the dynamic response of the joints are studied. The results showed that frequencies where peak amplitudes occurred were little dependent on the adhesive loss factor. However, peak amplitudes reduced for joints with a higher adhesive loss factor. Furthermore, the results indicated that for the joint geometries and properties investigated the system resonant frequencies were not affected by the presence of a central void covering up to 80% of the overlap length. In the experimental part, single lap joints were fabricated using 6061-T6 Aluminum. Adherents were joined together using Hysol EA 9689 adhesive film. Joints with various central voids were manufactured by removing adhesive film from the desired area of lap joints prior to bonding adherents. Dynamic responses of the joints were investigated using the hammer test technique. The system response was measured using both an accelerometer and a noncontact laser vibrometer. The natural frequencies of the joints obtained by using the laser vibrometer were very close to those obtained theoretically. However, natural frequencies obtained by using an accelerometer depended on the accelerometer location in the system, which was attributed to its mass contribution to the over- all system mass. A central void covering less than 80% of the overlap length had little effect on the system resonance frequencies. This was in agreement with the theoretical results. In contrast total system-damping ratios were a function of the void size. Joints without a void exhibited higher damping.

Aluminum brazed joints are used extensively in the automotive and aircraft industries. In order to insure the integrity of the bond, the effects of processing variables on the quality of the bond must be understood. The effects of brazing period and joint thickness on the microstructure, tensile properties, microhardness and micromechanisms of failure of two aluminum alloy 3003 plates connected by a layer of 4047 aluminum filler material were investigated. It was found that the amount of aluminum-silicon eutectic microstructure in the reaction zone decreased with increasing brazing period and decreasing joint thickness. This was attributed to silicon diffusion from the joint material and dissolution of base metal and its entrance into the liquid joint. The amount of shrinkage porosity in the reaction zone was found to increase with increasing brazing period due to base material solutioning. The ultimate tensile strength of joints decreased with increasing brazing period and decreasing joint thickness. This was attributed to the joint microstructure and shrinkage porosity formed in the joint. Shrinkage porosity was found to be the primary cause of decreased joint strength. Joints with 10 minutes brazing period failed within the base material, while for brazing periods greater than 10 minutes, joints failed within the aluminum-silicon eutectic microstructure of the reaction zone. This indicated that the joint strength was greater than the base material for joint with brazing period of 10 minutes. Finite element analysis was performed to determine the effect of joint material yield strength and joint thickness on the stress and strain field in the brazed joint. Finite element analysis results supported experimental observations.