The micro-structural strain response of tendon

Tendons are multi-level fibre-reinforced composites, designed to transmit muscle forces to the skeleton. During physiological loading, tendons experience tensile loads, which are transmitted through the structure to the cells, where they may initiate mechanotransduction pathways. The current study examines the structural reorganisation and resulting local strain fields within the tendon matrix under tensile load. It uses confocal microscopy to photobleached a grid onto the collagen and image its deformation under the application of incremental tensile strain. Six parameters are used to quantify fibril and fibre movement and examine the mechanisms of extension employed by fascicles. Results demonstrated an inhomogeneous strain response throughout the matrix and large variability between samples. Local strains in the loading axis were significantly smaller than the applied values. However, large compressive strains, perpendicular to the loading axis, were recorded. The average Poisson’s ratio (0.8) suggested cells may experience significant compression during loading. Deflection of the grid lines, indicating sliding between collagen fibres, and rotation of the grid were also recorded. These data highlight the non-homogenous strain environment of fascicles and provide further evidence for fibre sliding under tensile load. They also suggested a rotary component to tendon response, which may indicate a helical organisation to the tendon matrix.     

Micromechanical analysis of damage mechanisms in ceramic-matrix composites during mechanical and thermal cycling

This work presents a micromechanical study of the cyclic response of a undirectionally reinforced ceramic-matrix composite under time-varying load, parallel to fibres, and under thermal cycling. The analysis was based on the finite element method. The overall response was deduced from the response of a representative volume element consisting of concentrically placed cylinders of fibre and surrounding matrix, bounded axially by a matrix crack and a symmetry plane. The interface between the fibre and the matrix was assumed to be a frictional sliding contact (Coulomb friction). The results of this study indicated that the interfacial sliding stress τ_s may be assumed to be constant over the sliding distance, whereas its variation with the remote applied stress is important. It was also found that the overall stress/strain behaviour is non-linear when the state of interfacial sliding is changing, while a linear response results for a fully sliding interface. In the latter case, the tangential modulus in loading differs from that in unloading. For thermal cycling, the analysis showed that, due to insignificant interfacial sliding, the thermal expansion coefficients in the damaged state are practically the same as in the undamaged state.     

Constitutive modelling of arteries considering fibre recruitment and three-dimensional fibre distribution

Structurally motivated material models may provide increased insights into the underlying mechanics and physics of arteries under physiological loading conditions. We propose a multiscale model for arterial tissue capturing three different scales (i) a single collagen fibre; (ii) bundle of collagen fibres; and (iii) collagen network within the tissue. The waviness of collagen fibres is introduced by a probability density function for the recruitment stretch at which the fibre starts to bear load. The three-dimensional distribution of the collagen fibres is described by an orientation distribution function using the bivariate von Mises distribution, and fitted to experimental data. The strain energy for the tissue is decomposed additively into a part related to the matrix material and a part for the collagen fibres. Volume fractions account for the matrix/fibre constituents. The proposed model only uses two parameters namely a shear modulus of the matrix material and a (stiffness) parameter related to a single collagen fibre. A fit of the multiscale model to representative experimental data obtained from the individual layers of a human thoracic aorta shows that the proposed model is able to adequately capture the nonlinear and anisotropic behaviour of the aortic layers.     

The mechanical properties of composites manufactured from tendon fibres and pearl glue (animal glue)

The mechanical properties of a composite manufactured from bovine tendon and pearl glue (an animal glue containing gelatine and other proteins) are investigated. This composite was traditionally used in the construction of Asiatic re-curve bows for archery and is reputed to be tough yet elastic. Composites were manufactured by hand laying fibres into a mould and then pouring on hot glue. Tensile tests were performed on the specimens with the load being applied along the long axis of the fibres. The composite was found to absorb 18 MJ/m³ of energy to failure, comparable to carbon fibre composites, spring steel and butyl rubber. This energy absorption was achieved through the ductility and strength of the collagen fibres, which were found to be several times larger than the glue (fibre strength was 180 MPa, glue strength was 32 MPa, fibre failure strain was 26%, glue failure strain was 3%). However, the tensile modulus of the fibres and glue were similar. The composite was also found to be extremely damage tolerant, with many micro-cracks developing between strains of 2–20%, and dominated by elastic behaviour to surprisingly large deformations. The reasons for this are discussed.     

On the local elastic–plastic behaviour of the interface in titanium/silicon carbide composites

The purpose of this study is to conduct a high-resolution nonlinear finite element analysis of the elastic–plastic behaviour of titanium/silicon carbide composites subject to transverse loading. This class of metal matrix composites is designed for the next generation of supersonic jet engines and deserves careful assessment of its behaviour under thermo mechanical loads. Three aspects of the work are accordingly examined. The first is concerned with the development of a representative unit cell capable of accurately describing the local elastic–plastic behaviour of the interface in metal matrix composites under thermal and mechanical loads. The second is concerned with the determination of the influence of mismatch in the mechanical properties between the inhomogeneity and the matrix upon the induced stress fields and the plastic zone development and its growth. The third is concerned with unloading and the role played by the interface upon residual stresses. It is found that the maximum interfacial stress in the matrix appears in the case involving cooling from the relieving temperature with subsequent applied compressive loading. It is also found that the mismatch in mechanical properties between the matrix and the inhomogeneity introduces significant changes in the stress distribution in the matrix. Specifically, it is observed that the maximum radial and tangential stresses in the matrix take place at the interface. The plastic deformation of the matrix leads to a relaxation of these stresses and assists in developing a more uniform interfacial stress distribution. However, the matrix stresses and the resulting equivalent plastic strains still reach their maximum values at that interface. The results show similarities in the patterns of the interfacial stress distribution and plastic zone development for all ranges of fibre volume fractions and loading levels examined. However, they also show marked differences in both the magnitude and patterns of matrix stress distribution between the adjacent inhomogeneities as a result of interaction effects between the fibres.     

Cyclic load behaviour of reinforcing steel

The stress–strain behaviour of mild steel under cyclic loading is examined. The results of tests are described in which a variety of loadings were applied to reinforcing bars to study a range of initial strains and loading and unloading sequences from tension and compression. The tests emphasize that when postelastic stress reversals take place the stress–strain relationship for steel becomes non–linear over much of the loading range owing to the Bauschinger effect. It is found that a Ramberg–Osgood type function gives good agreement with the loading portions of the experimental curves except at very large strains. The empirical constants in the function were determined from the experimental results by least squares analyses and were found to depend on the plastic strain in the previous loading run and the number of previous loading runs.     

Extruded collagen fibres for tissue engineering applications: effect of crosslinking method on mechanical and biological properties

Reconstituted collagen fibres are promising candidates for tendon and ligament tissue regeneration. The crosslinking procedure determines the fibres’ mechanical properties, degradation rate, and cell–fibre interactions. We aimed to compare mechanical and biological properties of collagen fibres resulting from two different types of crosslinking chemistry based on 1-ethyl-3-(3-dimethyllaminopropyl)carbodiimide (EDC). Fibres were crosslinked with either EDC or with EDC and ethylene-glycol-diglycidyl-ether (EDC/EGDE). Single fibres were mechanically tested to failure and bundles of fibres were seeded with tendon fibroblasts (TFs) and cell attachment and proliferation were determined over 14 days in culture. Collagen type I and tenascin-C production were assessed by immunohistochemistry and dot-blotting. EDC chemistry resulted in fibres with average mechanical properties but the highest cell proliferation rate and matrix protein production. EDC/EGDE chemistry resulted in fibres with improved mechanical properties but with a lower biocompatibility profile. Both chemistries may provide useful structures for scaffolding regeneration of tendon and ligament tissue and will be evaluated for in vivo tendon regeneration in future experiments.     

Structure-mechanical properties relationship of natural tendons and ligaments

The mechanical characterization of rabbit Achilles' tendon and anterior cruciate ligament is presented. Both static and dynamic mechanical tests have been performed on fresh explanted tissues. Experimental results are presented and discussed in terms of a relationship between structural architecture and mechanical properties. The differences in collagen fibre configuration and composition between tendon and ligament influence the tensile and viscoelastic properties. In particular, tendons and ligaments showed a gradual transition from a rubber-like to a glassy-like behaviour during the loading process due to the traightening of collagen fibres.     

A study of damage development in a weft knitted fabric reinforced composite. Part 2: Stress–strain and early cyclic behaviour of composite laminates with realistic fabric layups

The mechanical behaviour of knitted fabric composites, consisting of four or five layers of weft knitted glass fabric in a Derakane vinyl ester matrix, has been investigated under simple tensile loading and in cyclic tests at increasing peak strains for a range of loading angles with respect to the wale direction of the knitted fabric. Stress–strain curves are non-linear from very low strains for all loading angles and they exhibit a rapidly reducing tangent modulus with increasing strain. Acoustic emission results and the results of the cyclic loading, together with comparisons with the results on the model specimens in Part 1, suggest the following sequence of damage development: damage develops initially between yarns at the loop cross-over points in the knitted fabric structure, progresses to the development of matrix cracking damage from these initiation sites at weak planes in the composite due to the fabric architecture, and then to the pulling out of loops across matrix cracks. The pulling out of loops across matrix cracks, together with matrix non-linearity, gives rise to a stress–strain curve with a very low tangent modulus at high strains and to hysteresis loops which do not close on unloading and reloading.     

Modeling hysteresis behavior of cross-ply C/SiC ceramic matrix composites

In this paper, the loading/unloading tensile behavior of cross-ply C/SiC ceramic matrix composites at room temperature has been investigated. The loading/unloading stress–strain curve exhibits obvious hysteresis behavior. An approach to model the hysteresis loops of cross-ply ceranic matrix composites including the effect of matrix cracking has been developed. Based on the damage mechanisms of fiber sliding relative to matrix during unloading and subsequent reloading, the unloading interface reverse slip length and reloading interface new slip length of different matrix cracking modes are obtained by the fracture mechanics approach. The hysteresis loops of cross-ply C/SiC ceramic matrix composites corresponding to different peak stresses have been predicted.     

Creep and creep-fatigue behaviour of continuous fibre reinforced glass-ceramic matrix Composites

The flexural creep and creep strain recovery behaviour during creep-fatigue tests of a cross-ply SiC fibre reinforced Barium Magnesium Aluminosilicate glass-ceramic matrix composite was investigated at 1100°C in air. Only heat-treated samples (1 h at 1100°C) were tested. Stress levels of 90, 105 and 120 MPa were examined to produce low strains (?0.4”?). A continuously decreasing creep strain rate with values between 1.6 × 10^?6 s^?1 to 4.7 × 10^?8s^?i at 120 MPa was observed with no steady-state regime. Extensive viscous strain recovery was found upon the unloading period during the short-duration cyclic creep (creep-fatigue) experiments. The creep strain recovery was quantified using strain recovery ratios. These ratios showed a slight dependence on the stress and cyclic loading frequencies investigated. The crept composites retained their ?graceful”? fracture behaviour after testing indicating that no (or limited) damage in the matrix was induced during creep and creep-fatigue loading.     

Influence of fibre and matrix failure strain on static and fatigue properties of carbon fibre-reinforced plastics

The potential benefits of the overall strength of carbon fibre-reinforced plastics with conventional matrix systems can only be realized to a relatively small extent in view of the fact that design criteria for CFRP components presently allow, for aerospace use, a maximum strain of about 0·4%. Under static loading conditions first matrix cracks must be expected in the transverse plies above 0·4% strain. Shifting the maximum allowable strain level to higher values would significantly increase the profitability of composites. It will be shown in the present paper that increasing the matrix failure strain (ductility) will yield a pronounced improvement of the mechanical properties (under static and fatigue loading) and a shift of the crack initiation level to higher strain values.

Further improvements of carbon fibres, to the extent of developing fracture strains of about 1·8%, require adapted matrix systems. In composites made from high-strain fibres together with a ductile matrix system further pronounced improvements in mechanical properties can be achieved.     

Characterization of fibre/matrix interfaces in carbon/carbon composites

The present paper proposes an approach to characterizing fibre/matrix (F/M) interface in carbon/carbon (C/C) composites with respect to both modes of loading that may be expected: opening or shearing. Push-out and tensile tests were used. The former tests involve the shearing mode whereas the latter ones involve the opening one. Push-out tests use a diamond indenter to load the fibres. The interface sliding shear stress was obtained from the load-fibre displacement curve. The tensile tests were conducted on specimens having fibres oriented at 90° with respect to loading direction in order to preferentially open the interfaces. Interface opening strength was extracted from the composite tensile stress–strain behaviour. The specimens were examined under load and after ultimate failure by optical microscopy (OM). The mechanical properties of the F/M interfaces were then discussed.     

Fibre-buckling in composite systems: a model for the ultrastructure of uncalcified collagen tissues

Rat tail tendon and other connective tissues are being studied as unusual fibre-filled composite materials of biological origin. The collagen fibres of these tissues follow a planar wavy course along the axis of the bundle of fibres, and the straightening of this waveform produces an initial “toe region” of low modulus in the stress-strain curve, followed by a linear high-modulus region associated with stretching of the fibres themselves. Presumably this mechanical behaviour is valuable to the animal as an impact absorption mechanism. Synthetic composite models of buckled high-modulus fibres in a soft elastic matrix have been made by differential shrinkage of the components, and show a waveform having several features in common with the collagen fibres in tendon. Both waveforms are planar, with a shape intermediate between a sine and a zig-zag. Parallel fibres buckle in phase and in parallel planes for fibre separations up to 10 diameters. When strained to high levels, both showed a previously unnoticed second waveform of smaller period superposed on the original waveform, due to slippage between the components. A possible mechanism for fibre bucklingin vivo is discussed.     

Analysis of the flax fibres tensile behaviour and analysis of the tensile stiffness increase

The knowledge of the behaviour of flax fibres is of crucial importance for their use as a reinforcement for composites materials. Flax fibres were tested under tensile loading and in repeated loading–unloading experiments. We have shown that fibre stiffness increases with the strain.This phenomenon is attributed to the orientation of the fibrils with the axis of the fibre when a strain occurs. By using micro-mechanical equations, the Young's modulus of a flax fibre is estimated by taking into account the composition of the fibre and the evolution of the orientation of the fibrils during a tensile test. A good agreement is found between experimental and calculated results. The origin of the large spread observed in the mechanical characteristics is analysed here.     

Effect of dynamic loading on tensile strength and failure mechanisms in a SiC fibre reinforced ceramic matrix composite

The tensile strength and associated failure micromechanisms have been characterized for a SiC fibrereinforced ceramic matrix composite subject to strain rates approaching 1000 s^–1. It is found that behaviour under such conditions is not described by the current matrix fracture/fibre pull-out models. This is a consequence of the rapid and extreme frictional heating produced at the fibre-matrix interface by sliding velocities on the order of 100 ms^–1. At sufficiently rapid loading rates, the near-interface matrix appears to melt, and the frictional interface shear resistance is reduced to the point that the fibres debond throughout the specimen, and pull out without failing. This suggests that for sufficiently rapid loading, the stress to fail the composite will approach that merely to create the initial matrix crack, i.e., a stress level well below the ultimate strength normally attainable under quasi-static conditions.     

Modeling Loading/Unloading Hysteresis Behavior of Unidirectional C/SiC Ceramic Matrix Composites

The loading/unloading tensile behavior of unidirectional C/SiC ceramic matrix composites at room temperature has been investigated. The loading/unloading stress–strain curve exhibits obvious hysteresis behavior. An approach to model the hysteresis loops of ceramic matrix composites including the effect of fiber failure during tensile loading has been developed. By adopting a shear-lag model which includes the matrix shear deformation in the bonded region and friction in the debonded region, the matrix cracking space and interface debonded length are obtained by matrix statistical cracking model and fracture mechanics interface debonded criterion. The two-parameter Weibull model is used to describe the fiber strength distribution. The stress carried by the intact and fracture fibers on the matrix crack plane during unloading and subsequent reloading is determined by the Global Load Sharing criterion. Based on the damage mechanisms of fiber sliding relative to matrix during unloading and subsequent reloading, the unloading interface reverse slip length and reloading interface new slip length are obtained by the fracture mechanics approach. The hysteresis loops of unidirectional C/SiC ceramic matrix composites corresponding to different stress have been predicted.     

Modelling the mechanics of partially mineralized collagen fibrils,fibres and tissue

Progressive stiffening of collagen tissue by bioapatite mineral is important physiologically, but the details of this stiffening are uncertain. Unresolved questions about the details of the accommodation of bioapatite within and upon collagen''s hierarchical structure have posed a central hurdle, but recent microscopy data resolve several major questions. These data suggest how collagen accommodates bioapatite at the lowest relevant hierarchical level (collagen fibrils), and suggest several possibilities for the progressive accommodation of bioapatite at higher hierarchical length scales (fibres and tissue). We developed approximations for the stiffening of collagen across spatial hierarchies based upon these data, and connected models across hierarchies levels to estimate mineralization-dependent tissue-level mechanics. In the five possible sequences of mineralization studied, percolation of the bioapatite phase proved to be an important determinant of the degree of stiffening by bioapatite. The models were applied to study one important instance of partially mineralized tissue, which occurs at the attachment of tendon to bone. All sequences of mineralization considered reproduced experimental observations of a region of tissue between tendon and bone that is more compliant than either tendon or bone, but the size and nature of this region depended strongly upon the sequence of mineralization. These models and observations have implications for engineered tissue scaffolds at the attachment of tendon to bone, bone development and graded biomimetic attachment of dissimilar hierarchical materials in general.     

Tension and flexural strength of silicon carbide fibre-reinforced glass ceramics

The use of silicon carbide-type fibres to reinforce lithium aluminosilicate glass ceramics results in composites with exceptional levels of strength and toughness. It is demonstrated that composite strength and stress-strain behaviour depend onin situ fibre strength, matrix composition, test technique and atmosphere of test. Both linear and non-linear tensile stress-strain curves are obtained with ultimate strengths at 22° C approaching 700 MPa and failure strains of 1%. Flexure tests performed at up to 1000° C in air are compared with data obtained in argon to demonstrate a significant dependence of strength and failure mode on test atmosphere. Finally, glass ceramic matrix composite performance is compared with a silicon carbide fibre-reinforced epoxy system to demonstrate the importance of matrix failure strain on strength and stress-strain behaviour.     

An experimental analysis of fracture mechanisms of short glass fibre reinforced polyamide 6,6 (SGFR-PA66)

In the present work, toughness of unfilled polyamide 6,6 (PA66) and short glass fibre reinforced polyamide 6,6 (SGFR-PA66) was investigated. Digital image correlation (DIC) was used with a single camera for in-plane displacement field measurement and then strain computation. The results allowed to extract the resistance curve for the PA66 and critical stress intensity factors, K_Ic, for the SGFR-PA66 with three glass fibre contents (15%, 30% and 50% (wt)) and under room temperature (20 °C). The tests were carried out on single edge notched tension (SENT) specimens. The DIC technique allowed to precise the spatial distribution of the local strains in a defined region including the crack tip at different steps of the loading. Scanning electron microscopy observations illustrated different damage mechanisms occurring in the studied composites: matrix crack, fibre–matrix interface failure and fibres pull out.