Humanitarian actors involved in physical rehabilitation, such as the International Committee of the Red Cross (ICRC), usually provide their beneficiaries with lower-limb prostheses comprising Solid Ankle Cushion Heel (SACH) feet as these are considered appropriate (price, durability, low profile to fit a majority of patients, appearance) and reliable for all ambulation levels. However, individuals in low-resource settings having higher ambulation abilities would greatly benefit from dynamic prosthetic feet with improved biomechanics and energy storage and release. Some attempts tried to address this increasing need (e.g. Niagara Foot) but most products proposed by large manufacturers often remain unaffordable and unsuitable to the context of low-resource settings. The design requirements and a price target were defined in partnership with the ICRC according to their initial assessment and used as a starting point for the development process and related technological choices. Numerical simulation and modeling were used to work on the design and to determine the required materials properties (mechanical, chemical, wear), and a cost modeling tool was used to select suitable materials and relevant processing routes (price vs. performance). A prosthetic foot comprising an internal keel made of composite materials, a filling foam, and a cosmetic shell with a foot shape was developed. Manufacturing processes meeting the cost criteria were identified and prototype feet were produced accordingly. These were successfully tested using a compression testing system before gait analyses were performed in the laboratory with non-amputees wearing testing boots. After validation in laboratory conditions, the prototype foot was tested in the field (Vietnam) with 11 trans-tibial unilateral amputees, who showed an increased mobility compared with the SACH foot. The collaboration of different research fields led to the development of a prosthetic foot which met the technical requirements determined by the ICRC's specific needs in its field of operation. The materials and selected production processes led to a manufacturing cost of less than 100 USD per part.

In this study, silica glass, optical fiber Bragg gratings (FBGs) are used for torque-induced strain monitoring in carbon fiber reinforced polymer (CFRP) hollow shafts toward the development of a methodology for structural load monitoring. Optical fibers with gratings are embedded during shaft manufacturing, by an industrial filament winding process, along different orientations with respect to its central axis and surface mounted after production. Experimental results are supported by numerical modeling of the shaft with appropriate boundary conditions and homogenized material properties. For an applied torque up to 800 Nm, the strain sensitivity of an embedded grating positioned along the reinforcing fibers’ direction winded under 55° is in the order of 3.6 pm/Nm, while this value is more than 4× times higher than the other examined orientations. The study also shows that surface-mounted optical fiber Bragg gratings along the reinforcing carbon fibers’ direction perform equally well in monitoring strains in composite shafts under torque.

Fibre composites (in particular carbon fibre reinforced polymers – CFRPs) are widely used in advanced applications because of their high specific strength and stiffness. However, their intrinsic laminated structure combined with the local mismatch of mechanical properties in mesoscale (due to different ply orientations) or constituents in microscale are responsible for their low toughness. Under applied mode I loading conditions, fracture of composites is accompanied of large scale bridging (LSB), greatly enhancing the resistance towards crack propagation. The phenomenon has been largely investigated on unidirectional (UD) laminates, using conventional double cantilever beam (DCB) specimen to quantify the evolution of the energy release rate (ERR). Numerous studies have also considered the fracture at interfaces between oriented plies, generally showing a stronger toughening effect than UDs, due to LSB. However, the published results are not conclusive and illustrate the difficulties to isolate the effect of ply-angles on both toughening and fracture mechanisms. In particular, fracture of selected antisymmetric interfaces showed distinctive behaviour with phases of stable and unstable crack growths [1]. The aim of the present study was to investigate the influence of plies’ orientation on the toughness and fracture morphology of antisymmetric interfaces [2].

Multidirectional laminates are very often used in advanced structures. However, the existing data in the literature regarding their fracture response is not conclusive. In this work, the fracture response of a +45∘//−45∘ interface is investigated under remote mixed mode loading and compared to a 0∘//0∘ layout. Several experiments were conducted under three mode mixities φ=0.15, 0.35 and 0.65 as well as pure modes I (φ=0) and II (φ=1.0) following the established standard procedures. Energy release rates were calculated using an appropriate reduced form of the J integral. Fracture toughness was independent of the interface at initiation but increased with mode mixity. Subsequent fracture resistance was negligible for the 0∘//0∘ layout, but increased significantly for the +45∘//−45∘ interface. Mechanistic investigations were carried out using X-ray computer tomography at 5 different load levels as well as transverse cross sections. The results showed lack of bridging in the case of 0∘//0∘ layout for all values of φ. For the +45∘//−45∘ interface, fracture was dominated by delamination, ply splitting and crack migration with their extent dependent upon φ. Numerical analyses based on the virtual crack closure technique demonstrated that the antisymmetric local fracture modes, interlaminar longitudinal shear vs. transverse shear, are responsible for delamination and crack migration, respectively. Based on the experimental observations, a mesoscale FE model was able to reproduce not only the failure mechanisms, i.e. delamination, transverse cracking and crack migration resulting in the zig-zag fracture pattern, but also give a reasonable approximation of the energy release rate obtained for each of the different mode mixities considered in this study.

Delamination is a well-known damage mode exhibited by laminated composites which has been extensively studied in unidirectional laminates (UD). In this work, a novel strategy consisting of the introduction of a small interlaminar defect to enhance the fracture resistance to delamination of UD composites is presented. This toughening concept is based on the simultaneous propagation of multiple interlaminar cracks along different interfaces. A preliminary numerical study showed that the minimum size required by the initial defect to trigger dual propagation was 4 times the ply thickness for intermediate and thin plies for any applied mixed mode, except for pure mode II. An experimental campaign to prove the toughening concept with 1 and 3 defects at adjacent interfaces was carried out and compared against a reference configuration under three different applied mode mixities (ϕglob=0.4,0.2 and 0). The single defect configuration reached an improvement in the fracture resistance of +300% under pure applied mode I, and +80% and +100% for applied mixed modes of 0.2 and 0.4, respectively. The configuration with 3 defects reached even higher fracture toughness values: +430% in pure applied mode I, and +115% and +100% for applied mixed modes of 0.2 and 0.4, respectively. A finite element model employing cohesive zones successfully predicted both, the phenomenon of multiple crack propagation, and the effective fracture resistance of the process. Interestingly, among the dissipation mechanisms reported experimentally, the extensive promotion of fiber bridging under applied pure mode I was observed, which was not reported in the baseline configuration.

Delamination is a very frequent damage mechanism that affects the integrity of laminated composites. In this study, the effect of ply orientation on crack growth resistance was analyzed for three different anti-symmetric interfaces (±30°,±45° and ±60°) and compared to a unidirectional baseline under remote mode II loading. Fracture toughness at initiation was the same regardless of the ply orientation, nevertheless, the energy dissipated during crack propagation increased with ply angle. The fracture process exhibited by the anti-symmetric laminates showed repetitive zig-zag patterns featuring simultaneous crack migration and delamination. A first set of numerical analyses based on the virtual crack closure technique (VCCT) revealed that the anti-symmetric local fracture modes, i.e. longitudinal shear vs. transverse shear, are responsible for delamination and crack migration, respectively. The main damage mechanisms and their evolution, as observed experimentally, were well reproduced by an appropriate cohesive zone model, which takes into account the ply orientation during delamination.

Delamination in composite materials is often accompanied by fiber bridging that increases resistance to crack growth. Here, delamination of two unidirectional carbon/epoxy systems was studied under monotonic and displacement-controlled fatigue loading. One material (CP004) presented a random distribution of fiber clusters and matrix-rich zones while the other (SE-84) had an ordered microstructure. The results showed that monotonic and fatigue delamination of CP004 presented similarities, with smooth crack growth and significant bridging. The SE-84 showed no bridging but matrix cohesive failure related to stick–slip growth under monotonic load and adhesive/cohesive failure with limited fiber bridging in fatigue. Data from embedded strain sensors showed that bridging under monotonic and fatigue were similar in CP004. The identified traction-separation relation under monotonic loads was used in a cohesive model to approximate the traction-separation at lower subcritical displacement, corresponding to crack arrest in fatigue. The results demonstrated that monotonic and fatigue delamination may have important similarities (or differences) depending on the microstructure and material properties.

Traction-separation relations due to large scale bridging in composites are very important in modeling their fracture response. Several works demonstrated that such relations are dependent upon the specimen's stiffness and loading conditions. Experimental data and micromechanics of bridging suggested that, in addition to the crack opening displacement (COD), the local curvature can be used as an additional kinematic parameter to incorporate the stiffness dependence on traction-separation-angle relations. In this work, analysis of data from DCB specimens with different stiffness, in three different materials, subjected to monotonic end opening forces, demonstrates that when the tractions are correlated with the product of local angle and COD, a stiffness independent traction-separation-angle relation is obtained, and can be implemented in an FE scheme. The methodology is further exemplified by fatigue data and fracture under pure moments that highlight the importance of the second kinematic parameter and the soundness of the approach.

In this work the differences in R-curve response and traction-separation relations due to a finite damage zone or large-scale bridging (LSB) in mode I fracture on double cantilever beams (DCB) were investigated under end opening forces (EOF) and pure moments (PM). To realize PM loading, a novel test-rig was designed, built and used to test adhesive joints with metallic substrates and unidirectional carbon fiber reinforced polymer (CFRP) specimens. In the adhesive joints, no pronounced difference was observed between the R-curves due to the two loading conditions. However, the experiments on the CFRP specimens showed important differences on both R-curve and traction separation relations due to LSB when comparing EOF and PM loading. These differences are attributed to the different curvature of the specimens’ arms in EOF and PM allowing for longer bridging zone in the latter case. The increase in the energy release rates was ~40% for the specimens subjected to PM with about four times higher maximum crack opening displacements at the steady state. Pertinent cohesive zone simulations predict the respone very well.

Thin-ply composites have gained a lot of interest in recent years thanks to their enhanced onset of damage, ultimate tensile strength and fatigue life as compared to their traditional counterparts. Regarding the onset of damage under tensile loading, in the transverse plies in particular, the underlying reasons of the enhanced strength and fracture properties were not yet well understood, especially for the thinnest plies available, as has been shown in Amacher et al. [1]. The acoustic emission (AE) measurements performed in this work raised the question of the applicability of the microscopy observations performed at the free edge of the samples for comparison with plane-strain models, and did not provide any information regarding the kind of damage dissipating the energy. Consequently, simultaneous in-situ optical microscopy images taken at the free edge of test samples and AE measurements were performed in this work to study the damage mechanisms of quasi-isotropic ([45/90/45/0]ns) unnotched tensile test samples. Ex-situ micro-tomography was then implemented to assess the damage propagation within the sample, and the acquired data were used to calibrate a pertinent embeddedcell multi-scale FE model [2].

The mode I delamination behavior of a unidirectional glass-fiber reinforced polymer with a prototype elasto-plastic polyurethane matrix (GF/PU) was investigated and compared with that of glass/epoxy (GF/EP) using double cantilever beam specimens. Fracture resistance was assessed using experimental data based on the strain energy release rate (ERR), G, calculated by means of the modified compliance calibration, and the J-integral, calculated using the applied force and arm rotations measured by digital image correlation. The fracture energies given by the two methods differed by similar to 5%. In both systems large scale bridging was observed and fracture resistance at initiation and steady state was about 4 times greater in GF/PU and correlated to adhesive failure in GF/EP and cohesive in GF/PU. Since the fiber sizing was the same, the higher ERR of GF/PU was attributed to strong glass/PU interface allowing higher local matrix strains and larger fiber bundles to develop. Traction-separation relations were determined by the direct and an indirect method using Fiber Bragg Grating sensors to construct numerical models to simulate the delamination process. The simulated force-displacement and R-curve data were in good agreement with experiments.

Lightweight design demands and complexity requirements of modern high-end structures in aerospace, automotive, sports and bioengineering can be successfully covered by a combination of fiber reinforced polymers (FRPs) with metallic components. Conventionally, mechanical locking is favored in integrating multi-material parts, avoiding bonded interfaces. The feasibility of a multi-material carbon FRP–aluminum structural component of a robotic exoskeleton, fabricated in a single step with the FRP directly cured on the aluminum domain, was investigated. To conduct the feasibility analysis, pertinent systematic FE modeling involving cohesive contact was employed to optimize the design, while strength and fracture testing were conducted to define the formed interfaces’ resistance. Sandblasting treatment was also investigated and compared with plain surfaces. The results show that the effect of residual stresses due to curing process governs the created joint’s durability. To reduce their effect, the local compliance of the multi-material components was altered by introducing a compliant layer along with modification of the aluminum domains’ local geometry in a manner that does not compromise the overall structural integrity. The interface stresses of the optimized geometry are a few times lower than the ones estimated for the initial design. The methodology adopted herein delivers some guidelines on treating such problems.

Fiber reinforced polymers (FRPs) subjected to mode I fracture show important toughening due to the development of large scale bridging (LSB). Experimental studies of this phenomenon in unidirectional carbon/epoxy laminates using double cantilever beam specimens, demonstrate important differences in R-curve response for inter- and intralaminar fracture. Post fracture observation of composite’s cross-section pointed out dissimilar fiber bundle size and shape, as the main origin of their differences. In the present paper, representative volume elements with the composite’s constituents, based on the actual material microstructure, and homogenized 2D finite element models were developed to study the effects of microstructure on the first stage of damage leading to LSB development in carbon/epoxy composites under mode I fracture. The differences between inter- and intralaminar fracture were investigated along with the influence of fiber dispersion and the presence of interply and intraply resin-rich zones. The numerical simulations captured different microcrack morphologies for inter- and intralaminar fracture, supporting the experimental observations, while parametric studies showed the influence of the microstructure in the formation of LSB. In particular, fiber dispersion within a ply and resin rich zone between plies play significant roles in mode I fracture and can be used to control toughening mechanisms in FRPs.

Thin-ply composites were shown to exhibit significantly delayed transverse cracking, but the linear onset of damage scaling with ply thickness reported by Amacher et al. (2014) did not correspond to the established LEFM based in situ strength model. This study further investigates this experimental behaviour by simultaneously comparing in situ free edge crack observation with acoustic emission measurements as well as performing ex-situ X-ray tomography observations of crack propagation. A multi-scale FE model was used to better understand the damage mechanisms at play, and showed a decreasing trend of the apparent toughness with decreasing ply thickness, which explains the deviation from the existing model. Transverse cracking at the free edges was observed to propagate quickly towards the center of the specimens for the thickest plies, while in the thinnest plies it is significantly delayed, up to a point where no cracks can reach the center of the sample before final failure.

Laminated composites are prone to fracture at layer interfaces. Such damage impairs their structural response and engenders important constraints in design. In this work, the influence of ply orientation on crack growth resistance was studied for three different antisymmetric interfaces and compared to a unidirectional reference one, using double cantilever beam specimens with equivalent stiffness, loaded under mode I conditions. Fracture toughness at initiation was found interface-independent. In all angle-ply specimens, distinct slow and fast phases of crack propagation were observed. Crack increments due to fast growth, were characterized using experimental energy release rates and verified from fracture surface analysis. The slow propagation phases were accompanied by large scale bridging involving intra-ply growth in the adjacent plies, with toughness increasing inversely with the angle. Mechanistic investigations suggest a consistent fracture pattern in terms of the interface angle. For each interface angle, a single traction-separation relation, obtained from the experimental energy release rate and crack opening displacements, was sufficient to model two consecutive slow propagation phases. These relations were used in 2D cohesive element models to predict very well the loading history.

In this paper the attention has been focused on the evaluation of how friction can influence Four-point End-Notched Flexure test in carbon fibre-epoxy composite materials. The starting point has been the hysteresis loop in the experimentally obtained Load versus Displacement curve due to an unloading-loading cycle. Different locations for friction have been considered. Numerical simulations have been performed by using Finite Elements and an experimental test campaign has been also carried out to validate the model and to optimize friction coefficients through the comparison with test results. The outcomes of the numerical analysis have given useful indications. Firstly, the comparison of the simulated maximum load and dissipated energy with those coming from the experimental tests has given good results. Secondly, it has been found that the contact between pins and specimens is the most significant location for friction.

Thin-ply composites represent a promising approach to further improve the performance of carbon fibre composite structures thanks to their ability to delay the onset of matrix cracking and delamination up to the point of fibre dominated failure. However, this increased strength comes with a more brittle failure response which raises concerns on damage tolerance. Thus a careful material optimization is needed to address this trade-off. In this work, eight different formulations of thin-ply composites ranging from low modulus to high modulus carbon fibres are evaluated to understand the effects of the fibre and matrix constituents on the onset of damage and strength in unnotched tensile (UNT) tests of quasi isotropic laminates for ply thicknesses between 300 and 30 microns. The obtained experimental data are combined in master curve diagrams for simplified material selection process. It is observed that certain thin-ply composites with a ply thickness t < 134 μm can reach UNT strength corresponding to or approaching the ultimate strain of the fibres as well as UNT stress at onset of damage as high as 92% of the latter. Based on this knowledge, a novel aerospace grade toughened thin-ply composite system is developed which can reach a quasi-isotropic UNT strength above 1 GPa (>95% of the fibre strain). The newly developed composite is further optimized to improve damage tolerance by toughening the resin and selected interfaces. The effect of those modifications on damage tolerance are evaluated through compression strength after impact (CAI) tests and open hole tensile tests (OHT). It is found that an optimized interlayer toughened thin-ply composite based on 68 microns plies of intermediate modulus fibre can reach both outstanding strength properties with comparable or better CAI and OHT strength compared to current aerospace grade composites.

The determination of the fracture toughness of fiber-reinforced polymers (FRPs) exhibiting significant nonlinear material behavior requires the use of methods that take into account the contribution of nonlinear phenomena on the computation of the crack driving force. While the J-integral method has been standardized (ASTM E1820) and extensively used to quantify the fracture toughness of homogeneous nonlinear materials, its validity to unidirectional FRPs remains uncertain. This work addresses this issue by comparing different methods to quantify the energy dissipation during fracture of glass fiber-reinforced polymers with a nonlinear polyurethane matrix. To this end, the J-integral under mode I transverse intralaminar crack growth is evaluated for the first time by directly computing J versus load-line displacement curves using strain maps obtained around the crack tip with digital image correlation. This direct approach is then compared with 2 established data reduction methods and data obtained from virtual tests to determine the suitability of standardized procedures to quantify the fracture energy of such heterogeneous materials. The results show that the best agreement among the values obtained with the different experimental methods is reached when the initial crack length accounts for 40 to 50% of the specimen's width. Accounting for the experimental uncertainties, the procedure described in the standard ASTM E1820 is suitable to quantify the fracture energy of unidirectional laminates displaying nonlinear mechanical response.

This book presents the basic concepts for the mathematical modeling of classical solid and fluid continuous media. It consists of eight chapters treating, Cartesian tensors, the kinematics, and dynamics of a continuous medium, thermodynamics, constitutive equations of classical Newtonian fluids and elastic solids, introduction to the linear theory of elasticity as well as Newtonian fluid mechanics. In each case, simple application examples provide analytical solutions that illustrate the power of modeling using continuum mechanics principles. Appendices give the necessary additions to follow the work and represent the field equations in cylindrical and spherical coordinate systems. Each chapter proposes a series of exercises and suggestions for their solution is also provided. Clear and educational, this book is intended for engineering and physics students who want to learn the basic principles of continuum mechanics. The subject is developed in a simple-to-follow pedagogical manner that readers can work through on their own. They will find in this work a complete modern introduction that opens the door to this vast territory of knowledge.

Fiber bridging is one of the main toughening mechanisms in mode I interlaminar and intralaminar fracture of laminated composites. Intact fibers exert closing forces on both faces of the crack, restraining crack propagation. An effective identification procedure is required to characterize bridging tractions and to develop accurate prediction models. The method proposed in this work is based on the resistance (R)-curve and assumes fiber bridging tractions decreasing non-linearly with respect to the crack opening displacement, following a parametric function. The distribution parameters are identified by a fixed-point iterative procedure where the energy release rate computed in a numerical model is matched with the values obtained experimentally in two points of the R-curve. The method is applied and validated through three cases, from low bridging intensity in thin-ply delamination to high bridging intensity in intralaminar fracture.