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Three-point and four-point bending tests were carried out on sandwich beams consisting of glass-fibre-reinforced plastic facings and a Divinycell H60 foam core. During the tests, final failure was invariably precipitated in the upper facing at the points of load introduction, whereas no other failure modes typically exhibited by a sandwich structure were observed. From the experimental results, the critical load causing final failure was found to be independent of the overall bending moment M and local force P l alone, in contrast with the hypotheses of the theoretical models presently available in the literature. On the contrary, for a given M / P l ratio adopted in the tests, the critical conditions were achieved more easily in the case of four-point than under three-point bending. A possible explanation of the observed phenomenon was given by calling into question the influence of the shear force, that may contribute to the sandwich local collapse. An empirical failure criterion, taking into account the bending moment, the local force and the shear force, was found to reasonably match the experimental results, although the physical meaning of one of the parameters appearing in the model formulation is matter of further research.

Natural fibre composite have a potential to be widely applied in the alternative to a fibreglass composites in sustainable energy impact absorption structures. In this study, the behaviour of hemp fibre epoxy composites subjected to a low-velocity impact loading, using an instrumented falling weight impact equipment, is presented. Two types of hemp reinforcements were used: unidirectional and bi-directional fabric and three balanced laminates (0°/90°) different in thickness were studied: 4 plies, 8 plies, 12 plies. The results were compared. The laminates were fabricated by RIFT process using a common epoxy matrix. The reached volumetric fibre percentage V f was not too high. It assumed a value of 34% for the unidirectional reinforcement and an average value of 30% for the bidirectional one. Some laminates were impregnated by PLA resin at the aim to obtain a completely natural system. The impact behaviour was analysed carrying out tests impacting square specimens, 100 × 100 mm, with a hemispherical tup geometry with a diameter of 19.8 mm and a velocity of 4.0 m/s. Both penetration and indentation tests were performed at the aim to investigate about the damage start and evolution. The impact induced damage, characterised by an optical microscope, includes matrix cracking, delamination, fibre breakage and fibre pullout. An interesting compressed central zone of the laminate under the impact point was noted.

Low-velocity impact tests were carried out on sandwich plates having CFRP facings and thin rubbery core. Two types of cores, differing in the material nature and thickness, were used. For comparison, similar tests were performed on the monolithic laminate. Various impact parameters, among which indentation, first failure energy, perforation energy, absorbed energy and maximum contact force, were analyzed, to highlight the effect of the core on the material response. The influence of the core on the macroscopic behaviour of the panels was quite limited, except in the elastic phase, where the lower stiffness of the sandwich configurations resulted in a higher energy at first failure. More relevant differences were found from the study of failure modes, carried out combining ultrasonic C-scan and a limited number of microscopic observations. In particular, in correspondence of the energy for barely visible impact damage, besides considerable facing-core debonding, both the facings of the sandwich structures exhibited fibre breakage at their back side.

Low-velocity impact tests were carried out on stitched carbon fibre-reinforced plastic laminates of various thicknesses, whose behaviour was studied with reference to the overall force–displacement curve, first failure load, penetration, indentation and damage extent. The results obtained were compared with similar data available for 2D laminates. Apparently, the presence of stitches did not affect substantially the material behaviour in terms of force–displacement curve, first failure load, and indentation. However, the stitched laminates exhibited a penetration energy about 30% lower than their 2D equivalent. Further, the advantage of stitching in terms of impact damage resistance was evident only for high thickness composites. The data generated suggest that the use of stitches could be unnecessary to hinder delamination in thin 2D laminates.

The scope of this paper was to establish a correlation between the damage occurring in a composite as a consequence of low-velocity impact and the energy dissipated during the impact phenomenon. To this aim, instrumented impact tests were carried out on glass fabric/epoxy laminates of three different thicknesses, using different energy levels. The irreversibly absorbed energy was obtained from the force–displacement curves provided by the impact machine. To assess damage progression as a function of impact energy, ply-by-ply delamination and fibre breakages revealed by destructive tests were measured. A previous model, based on energy balance considerations, was applied to interpret the experimental results, together with an original method of data reduction, allowing for the isolation of the maximum energy portion due to indentation and vibrational effects. From the results obtained, the contribution of fibre breakage and matrix damage to the irreversibly absorbed energy is comparable at low impact energies; with increasing initial energy levels, delamination becomes predominant in determining energy dissipation. However, the critical energy-release rate required to propagate delamination, as calculated from impact data, is considerably higher than the typical values deriving from Mode II delamination tests performed under laboratory conditions.

The empirical model recently found by the authors for the prediction of the indentation depth was verified for composite laminates different in matrix and fiber subjected to low velocity impact loads. The data obtained in a previous research on common glass and carbon fiber laminates made by commonly used epoxy matrix, were here compared to the results obtained on laminates made by glass fibers immersed in phenolic matrix and novel basalt fibers immersed in epoxy resin. The model takes into explicitly account the tup diameter and presents the advantage that only a single material constant to be experimentally determined is necessary for the prediction. The comparison showed that the value of the constant is different for the different material systems analyzed so that it can be assumed as an index for the indentation sensitivity. POLYM. COMPOS., 36:987–991, 2015. © 2015 Society of Plastics Engineers

Mechanical tests were carried out on a fibreglass/aluminium hybrid laminate, made of 0/90 S2-glass/epoxy laminae and Al 2024 T3 sheets, in order to find its tensile stress–tensile strain curve, residual tensile strain in correspondence of predetermined normal stress levels, and shear stress–shear strain curve. The basic layers were also suitably characterized, and a moderate anisotropy, reflecting the fabrication process, was found in the metal sheets. To theoretically predict the laminate response, classical lamination theory was modified to account for the inelastic behaviour of aluminium, which was substituted by an “equivalent” material governed by a simple constitutive law. Final failure conditions were calculated by assuming the maximum strain criterion and Tsai-Hill criterion for aluminium and fibreglass, respectively. Comparing the theoretical predictions with experimental results, it was concluded that the model adopted describes with sufficient accuracy the overall tensile stress–tensile strain curve, as well as the residual strains and the shear stress–shear strain response. The aluminium anisotropy influenced the tensile behaviour, markedly affecting the yield stress value, as also predicted by the analysis. Because of the complex phenomena occurring during final failure, the agreement between theory and data was only fair when the calculation of the tensile strength and failure strain was attempted. The material shear strength could not be determined, since the Iosipescu device used proven inadequate to result in material failure.

The effectiveness of a new empirical model, aiming to predict the indentation depth resulting in a composite laminate from a hemispherical tup impacting it at low velocity, is here proposed. With this simple model including only the diameter of the impactor and the ratio between the impact energy and the perforation one, a material-independent parameter characterising the indentation depth is identified. Several samples with different thicknesses, impacted by various impactor tips, are tested for estimating this parameter. To reach the above mentioned scopes, low velocity impact tests were carried out on two different composite systems with different stacking sequences, thicknesses and fiber volume fractions: (a) glass/epoxy prepreg; (b) graphite/epoxy prepreg. The samples were simply supported on steel plates or clamped and they were struck at the center by hemispherical steel noses having 16 and 19.8 mm diameters. After impact, indentation was measured according to EN 6038 standard. The CFRP indentation data were drawn from a database: about 200 test records, generated by various researchers were individuated. The advantages of the new model are that the effect of the tup diameter is explicitly accounted for. Furthermore, a single material constant has to be experimentally determined and it can be assumed as an index for the indentation sensitivity, on the basis of which different materials can be ranked. The constant was found similar for GFRP and CFRP laminates denoting independence of constraint conditions, laminate type or laminae orientation and stacking sequence. POLYM. COMPOS., 34:2061–2066, 2013. © 2013 Society of Plastics Engineers

Glass fibre-reinforced plastic beams were pre-fatigued in four-point bending up to selected portions of their fatigue life. The samples were then monotonically brought to failure while recording their acoustic emission response. The trend of the cumulative event counts was markedly affected by the specimen load history: for a given stress level, a higher activity was obtained from samples subjected to a higher number of cycles. A good empirical correlation was found between the material residual strength and the total event counts detected at maximum stress applied during pre-fatiguing cycles. Moreover, the correlation was improved when a previous model, relying on fracture mechanics concepts, was utilised. However, in both cases, a difficulty was experienced in evaluating the residual strength of the composite laminate after a small number of fatigue cycles. Under these conditions, the modulus decrease was seemingly more sensitive to the effects of fatigue than the acoustic emission response.

Low-velocity impact tests were performed on fibreglass–aluminium composites made of 2024 T3 sheets and S2-glass/epoxy prepreg layers, using an instrumented falling weight machine. For comparison purposes, similar tests were carried out on monolithic 2024 T3 sheets of equivalent thickness. In the tests, the impact speed, mass, and energy were varied, to ascertain the influence of these parameters on the material response. From the results obtained, the overall force–displacement curve only depends on the impact energy, rather than on the mass and speed separately. Further, the energy required for penetration is higher for monolithic aluminium than for the fibreglass–aluminium. However, the latter material seems to offer better performance than carbon fibre- and glass fibre-reinforced laminates in terms of penetration energy, damage resistance, and inspectability. The main failure modes of fibreglass–aluminium were assessed by both ultrasonic C-scan and chemical grinding of aluminium sheets. It was found that the energy required for first failure is very low, whereas the energy level resulting in first fibre failure is similar to that inducing first cracking in the 2024 T3 sheets. From the experimental data, simple empirical relationships were found for the calculation of maximum contact force, energy, and residual displacement as a function of the maximum displacement.

Acoustic Emission (AE) has long been recognized as a viable technique for real-time monitoring of metallic and composite structures, giving useful information not only on the presence of defects, but also on their criticity. Compared to other Non-Destructive Testing methods (NDTs) AE offers the advantage to locate defects in real time. The acoustic wave emitted by a source, related to a damage start or propagation, travels inside the material and it is received in different time by acoustic sensors arrayed on the surface. Knowing the different arrival times it is possible to locate the emission source position by the triangulation technique. For homogeneous material, this technique is easy to develop. However, the anisotropy nature of a composite material does not allow to have the same sound velocity in all the directions, so the development of mathematical models and algorithms for the implementation of the triangulation technique is difficult to set up. Since the above mentioned problem, this work proposes an alternative method to locate the point of an event on CFRP plates by analyzing the time of arrival of the ultrasonic signals received by three passive sensors attached to the plate surface in a known triangular configuration. The method is based on a simple concept: the comparison between the three measured arrival times and the predicted ones by analytical formulations. It was applied and validated through experimental tests carried out on a square unidirectional carbon fibre laminate. From the results, a good agreement between the predicted and the real position of the sound source was found.

Three-point bending tests in the elastic domain were carried out on sandwich specimens with the facings made of unidirectional T800H/3900-2 laminates, and the core of a soft and thin viscoelastic layer, varying the slenderness ratio. A closed-form formula available in the literature, developed for sandwich beams with thick facings, was used to predict the rigidities in flexure, adopting three different methods for the calculation of the shear rigidity. The best results were obtained by the classical sandwich theory, which provided reasonably good correlation with the experimental results, slightly overestimating the actual values. A finite element model consisting of three layers, made of standard CQUAD4 and CHEXA8 elements for facings and core, respectively, was developed, accurately predicting beam bending behavior. From the numerical results, the inability of classical sandwich theory to correctly estimate the bending rigidity is correlated with the through-the-thickness shear deformation of facings, not accounted for in the analysis.

Static tests were carried out on circular carbon fibre reinforced plastic plates of various thicknesses, which where loaded at the center by a hemispherical steel indentor. The tests were stopped at predetermined values of the displacement, and the indentation after the loading stage was evaluated. Tests were also performed up to complete penetration, using different indentor diameters. The data generated were compared with similar results previously obtained under low-velocity impact conditions, and treated according to models developed for the dynamic case. Apparently, both the penetration energy and indentation were not affected by the loading speed. The new experimental results showed that an empirical law previously proposed by the authors, aiming to predict the indentation as a function of the absorbed energy, is inaccurate when high energy levels are imparted to the material. A new empirical law, more efficient than the earlier, was assessed. The data collected indicate that the constants appearing in the new model are negligibly influenced by the laminate type and thickness, and constraint conditions adopted.

Laser marking tests were carried out on AISI 304 steel, using a Q-switched diode pumped Nd:YAG laser. The aim was to determine the correlation occurring between working parameters (i.e. pulse frequency, beam scanning speed, and current intensity) and resulting mark visibility. The latter was evaluated as the contrast index measured from digital images of the marks. To characterize mark features, its width and roughness were estimated, and analyses employing optical and scanning electron microscopy coupled with energy dispersive X-ray technique were carried out. From the experimental results, both surface roughness and oxidation increased as a function of frequency, resulting in an improvement in contrast, up to a characteristic value, decreasing afterwards. Besides, the maximum visibility value was beneficially affected by lower scanning speeds and lower current intensities. An empirical model was built, and from it the best processing conditions for optimum mark visibility, taking into account the operating constraints of the laser system used, were drawn.

Long-term orthogonal cutting tests were carried out on sheet moulding compound, using high speed steel tools with 0° rake and 5° relief angle and a constant depth of cut, in order to verify the effect of tool wear on cutting forces. The tests were periodically interrupted, and the variation of cutting forces as a function of depth of cut at various degrees of wear was measured. It was observed that the thrust force is much more sensitive to wear than the principal one. The tool wear features suggested negligible sliding of the chip against the tool face, and intense friction along the tool flank, in agreement with previous results concerning the machining of unidirectional carbon-fibre-reinforced plastics. Accordingly, a force model previously proposed for unidirectional composites was applied to the cutting data. It was found that the increase in the principal force with wear is attributable to the increase in the thrust force generated at the tool flank, whereas the force arising at the tool face is substantially unaffected by tool wear. This allowed for the definition of a unit cutting force independent of both the depth of cut and the tool wear.

Static and fatigue tests were carried out in four-point bending on three random Glass Fibre Reinforced Plastics (GFRP), different in resin type (thermosetting and thermoplastic), resin content, and fibre form. The experimental results were evaluated in the light of a recent two-parameter model, allowing for a statistical analysis of the fatigue data. It is shown that, despite the different nature of the materials considered, the theoretical model accurately predicts the fatigue response, permitting the calculation of the scatter in fatigue life from the scatter in static strength. A physical interpretation is given for the two parameters appearing in the model, correlated with the material sensitivity to stress amplitude and number of cycles, respectively. From the values of the two parameters, evaluated for the GFRPs tested, a common trend is observed: the higher the material sensitivity to stress amplitude, the lower its sensitivity to number of cycles. This implies that comparing different materials on...

Static and fatigue tests have been performed in four-point bending on a random continuous-fibre-reinforced polypropylene. The data obtained were used to assess a closed-form formula, previously presented, aimed at the prediction of the fatigue response of a composite material, and explicitly accounting for the effect of the stress ratio. Comparing the experimental results with similar data available in the literature for thermoset-based composites, it was shown that the presence of an inherently ductile, thermoplastic matrix does not sensibly affect the fatigue sensitivity of the material, probably because of the constraint action of the reinforcement. From the fatigue model, a statistical model was developed, assuming a distribution of the static strength according to a two-parameter Weibull distribution. The data were in excellent agreement with theoretical predictions, indicating that a fatigue characterisation for probabilistic design can be achieved by a minimum of experimental tests.

Artificial neural networks (ANNs) were used to predict the residual strength of glass fibre-reinforced plastic beams pre-fatigued in flexure up to different portions of their fatigue life. To this aim, the acoustic emission signals recorded during the tests for the measurement of the residual strength, and the associated applied stress, were provided as input. An optimisation of the network configuration was carried out, using the root-mean-square error calculated in the training stage as the optimisation parameter. The predictive accuracy of the optimised ANN, consisting of two nodes in the input layer, four nodes in the hidden layer, and a single node in the output layer, was tested by the “leave-k-out” method. From the results obtained, ANN provided quite reliable predictions when the applied load was sufficiently far from the failure load, performing better than a previous theoretical model, relying on fracture mechanics concepts. Therefore, ANN was shown to be a valid tool in the non-destructive evaluation of composite materials employed in fatigue-sensitive applications.

Orthogonal cutting tests were carried out on unidirectional glass fibre-reinforced plastic composites, holding the cutting direction parallel to the fibre direction. The tools were made of high speed steel, with rake angle α = 0°; two relief angles γ, namely 7° and 15°, were adopted. A very low cutting speed was utilized, in order to avoid thermal effects on both the tool and the work material. The experimental results show that, under the selected operating conditions, the tool wear essentially consists of a very rapid rounding of the tool nose (nose wear). The face wear evolution is practically independent of the relief angle, whereas the latter affects the flank wear rate, which is slightly lower for the higher γ value. Both the horizontal and the vertical cutting forces exhibit notable increases with tool wear. The force data are interpreted in the light of a previously presented model, aiming to predict cutting forces as a function of the cutting parameters. It is shown that the observed increase in the horizontal force can be simply attributed to the increase in the vertical force at the tool flank, whereas the chip-tool interaction forces occuring at the tool face seem to be unaffected by wear phenomena. Finally, a strict correlation is found between the flank wear and the recorded vertical force variations.

This paper deals with tensile testing of GRP laminates containing impact damage generated with different impact energies. Acoustic emission (AE) detection and analysis was used to attempt the prediction of residual tensile strength after impact (RTSAI). A modified version of a previous model for residual strength evaluation of center-hole composite laminates is proposed. Its rationale is the introduction of a non-dimensional stress to make the composite laminate AE response independent of damage geometry. The experimental results show that AE activity is strictly correlated to RTSAI rather than to impact energy. Experimental agreement with the model is verified for both impacted and center-hole composite samples.

The paper deals with the design of a composite arm, to be employed in the architecture of industrial, measuring robots. Based on the real working conditions, the arm is reduced to a cantilever beam, shaped as a thin walled tube, supporting a mass at the free end. An optimization study is carried out, aiming to determine the laminate properties capable of providing the maximum fundamental frequency (FF) in bending. The optimization relies on an approximate solution, obtained by modifying the Rayleigh energy method to account for the shear effect. It results in a closed-form formula, explicitly correlating FF with composite elastic properties. Two classes of laminates, namely (± θ) s and ( 0 ± 45 n ) s , are examined in order to assess their ability to fulfil the requirement of a maximum FF value. Moreover, the advantages and drawbacks of composites compared to metals are highlighted for the application under concern. Finally, the validity of the proposed solution is demonstrated by comparison with the results of a finite element analysis.

Residual strength prediction through acoustic emission (AE) detection and analysis is attempted for tensile loading of GFR composite laminates containing center holes. By utilizing a previously developed two-parameter fracture mechanics model, the mechanical behavior of circular center hole composite specimens was interpreted. The AE response of the specimens was shown to be controlled by stress intensity factor K, rather than stress. In order to establish a quantitative basis for AE analysis aimed at predicting the fracture behavior of center hole composite laminates, a description of the experimental AE response through a mathematical model was considered necessary. An analytical expression of exponential form was assumed and experimentally verified. The excellent agreement between theory and experiment quantitatively confirmed the validity of the model. Through AE detection and analysis, it is therefore possible to assess hole criticality in composite laminates by direct prediction of their residual strength under tensile loading.

Low velocity, instrumented impact tests were carried out on sandwich panels made of glass fiber reinforced plastic facings and polyvinylchloride foam core. Three different core densities and three core thicknesses were examined. A damage parameter D was defined to account for the fiber damage size as evaluated through visual inspection. The experimental results demonstrate that D depends only on impact energy, whereas it is substantially independent of core density and thickness. An explanation for this behavior is formulated on the basis of recorded impact history. The results of tensile tests, performed to assess the residual strength after impact of the facing material, were analyzed using a previous model, modified according to the findings of an experimental work carried out by Cantwell and Morton. A correlation is found between the strength loss determined by impact damage and artificially implanted circular holes. Accordingly, a procedure is presented to allow for an accurate prediction of residual strength after impact as a function of kinetic energy. Finally, it is shown that residual strength can be reasonably predicted on the basis of damage parameter D, although in some cases this can result in a nonconservative estimate of the composite load-carrying capability.

Flexure tests in three-point bending were performed in the elastic domain on sandwich specimens whose facings were made of T800H/3900-2 laminates, and the core by a soft rubbery layer. The contribution of the shear and flexural deformations to the overall deflection was varied by varying the slenderness ratio. The rigidities yielded by the load-displacement curve were corrected for the indentation occurring at the points of load introduction, using an experimentally determined calibration curve. Due to the thinness of the sandwich, indentation negligibly affected the precision of the results, with the apparent rigidities differing from the actual ones by less than 2%. By an analytical formula previously developed for sandwich structures, a prediction of the rigidities in flexure was attempted, adopting elastic constants available in the literature. The correlation with the data points was poor, with the theoretical results largely overestimating the actual rigidities. However, the reliability of the closed-form formula was supported by finite element analysis, carried out modelling the facings by 2D plate elements, and the core by 3D brick elements. Through the formula, the core shear modulus was individuated as responsible of the discrepancies observed. Assuming a suitable value for this parameter, both the analytic solution and the finite element models were able to match with accuracy the rigidities measured.

Three-point bending tests in the elastic domain were carried out on unidirectional laminates made of T800H/3900-2 laminae, holding the fibre direction coincident with the longitudinal axis of the beam. The slenderness ratio was varied in the range 10–65, in order to highlight the contribution of the shear deformation to the structural response. Local rigidity tests were also performed, to ascertain the influence of the indentation at the loading points on the rigidities measured. From the results obtained, the effect of the local deformation on the apparent flexural rigidity was the higher, as the slenderness ratio was reduced, with errors as large as 18% for the shorter spans adopted. Using Timoshenko’s beam theory and finite element analyses, a prediction of the rigidity in flexure was attempted. The theoretical results and the experimental data showed an excellent correlation, provided an unexpectedly low value of the through-thickness shear modulus was assumed in the calculations. Possible reasons for this occurrence were pointed out, involving the role played by the epoxy/polyamide interleaves in the behaviour of the material, as well as the actual shear correction factor to be used to take into account the shear effect.

This paper deals with the measurement of mode I interlaminar fracture toughness, Glc, of composite laminates by using double cantilever beam (DCB) specimens. It is shown that a formula commonly used for data reduction, based on linear elasticity, may result in small errors in calculating Glc, even when marked non-linearities in the load-displacement curve are observed, because of the adoption of thin samples. The implications of this finding for the design of the DCB specimen are discussed; furthermore, some experimental results are presented, for graphite/epoxy composites, which confirm theoretical predictions.

Monotonic and tension–tension fatigue tests were carried out on E-glass chopped-strand-mat/polyester composites, varying the flexibiliser content by weight in the matrix in the range 0–30%. The flexibilising action was due to the adipic acid monomers present in the flexibiliser. In monotonic tests, the most marked effect of resin flexibility was in the transverse cracks formed during loading, whose critical density (i.e., the density at failure) was very high for the rigid matrix, resulting in a highly non-linear stress–strain curve, and in the largest apparent strain to failure. With suitably increasing the flexibiliser content, the transverse crack formation was nearly suppressed, and the overall stress–strain curve approached linearity. In fatigue, the critical crack density decreased with increasing fatigue life in the case of the rigid matrix. For the flexibilised resins, the crack density at failure was independent of the maximum applied stress, larger than observed in monotonic tests, and higher the higher was the flexibiliser content, up to about 80% of the tensile strength. Beyond this limit, it converged through the material monotonic behaviour. The evolution of the residual elastic modulus with elapsing fatigue cycles was qualitatively consistent with the number of transverse cracks observed. The more flexible the matrix, the lower was the fractional modulus loss in fatigue. However, the highest elastic modulus along all the fatigue life pertained to the composite with rigid matrix, due to the flexibiliser adversely affecting the initial rigidity. Despite the differences in monotonic response and crack formation features, all the materials tested exhibited very similar S – N curves at moderately high fatigue lives. Nevertheless, appropriately treating the experimental results in terms of fatigue sensitivity, it was found that this parameter tends to increase with increasing matrix flexibility.

An experimental investigation was carried out on a fibreglass/aluminium (FGA) laminate in order to characterise its behaviour under pin- and bolt-bearing conditions. In pin bearing, the limit width-to-diameter and edge distance-to-diameter ratios necessary to avoid unsafe failure modes were lower than those usually quoted for classical laminates. A simple model to design safe pin-bearing joints, previously proposed for fibre-reinforced plastics, was effective also for the FGA. The study of the failure modes suggested that the aluminium layers play a major role in determining failure. The latter was due to the shear buckling of the individual laminae, which were decoupled from each other by extensive delamination/debonding phenomena. Under bolt-bearing conditions, the features of the load–displacement curve allowed for the individuation of two bearing strengths, labelled as ‘damage-bearing strength’ and ‘failure-bearing strength’, respectively. The damage-bearing strength was substantially unaffected by the bolt torque, and was up to 20% higher than the pin-bearing strength. The failure-bearing strength slightly increased with increasing the clamping pressure, achieving values up to 85% larger than the pin-bearing strength. From the microscopic failure modes observed, a possible explanation for the two bolt-bearing strengths recorded was given.

Monotonic tensile tests were carried out on a polyester orthophthalic resin with various contents of flexibiliser, using two loading speeds. All the main mechanical parameters characterising the tensile material behaviour, i.e. the elastic modulus, strain to failure, and strength, were affected by the flexibiliser content and strain rate. In particular, increasing the flexibiliser content and decreasing the strain rate resulted in a higher strain to failure and a lower elastic modulus. On the contrary, the tensile strength reached a maximum in correspondence of a flexibiliser content specific of the loading speed adopted. The different resin formulations were characterised in tension–tension fatigue. Many qualitative correlations were found between the experimental S–N curves of the resins and those of composite materials. In fact, their trend was well described by a fatigue model assessed for composites, and their scatter in fatigue was consistent with the strength-life equal rank assumption. The fatigue sensitivity was affected by the flexibiliser content, but did not vary monotonically with the latter. The curves of fatigue life were very different depending on the fact that the stress or the strain was used as the ordinate. Nevertheless, the feature common to both cases was the seeming convergence of all the fatigue curves when 10 6 cycles were approached, similarly to what usually occurs for composites.

This work was devoted to the prediction of the elastic energy stored at first failure in a circular composite plate statically loaded at the centre. To describe the load‐ deflection curve, a previous model was further developed, to explicitly account for the tup diameter. The first failure load was calculated through a simple formula, available in the literature, which was suitably varied. An original expression was derived for the energy at first failure. The experimental tests were carried out on carbon fibre reinforced plastic laminates of various thicknesses, which were simply supported at the periphery and loaded using different support and indentor diameters. The results obtained show that the elastic model, which takes into account the non-linearity deriving from large displacements and local indentation, is very accurate in shaping the load ‐deflection curve up to the first failure point. In general, also the predicted load and energy at first failure are in good agreement with the corresponding measured values. Both theory and experiments demonstrate that the critical load is independent of the support diameter, whereas it increases with increasing the plate thickness and the indentor diameter. When the support diameter and thickness increase, the energy at first failure increases as well. A particular condition, resulting in the failure of the force model, is achieved when the curvature of the plate at first failure is considerable. In this case, critical forces notably higher than expected from theory are measured. A possible explanation for this behaviour is given. q 2003 Elsevier Science Ltd. All rights reserved.

Contrary to metals, composite materials suffer not only a strength, but also a modulus decrease when subjected to cyclic stresses. Therefore, establishing a correlation between the fatigue parameters and the modulus degradation becomes important in stiffness-critical design. Besides, the knowledge of the law governing the modulus decay would be a powerful tool in predicting the residual fatigue life through simple non-destructive tests. The material tested in this work was polypropylene charged with CaCO3 mineral filler, often employed in household appliances for its attractive properties, such as good mechanical properties coupled with low density, high damping, good acoustic isolation, high chemical stability and low cost. Rectangular specimens were fabricated by injection molding and loaded in simple bending under displacement control at low frequency, to avoid excessive heating. Four different maximum displacement values were selected, and for each the modulus decrease was monitored periodically, to assess its variation with cycle evolution. As expected, the modulus decay was the more evident, for a fixed number of cycles, the larger was the maximum displacement imparted in fatigue. To analytically express the decrease in modulus as a function of cycles elapsed, a simple two-parameter model available from the literature was assumed and suitably modified. From the data generated, the formula was able to describe the modulus variation in fatigue; however, the parameters appearing in it were strongly dependent on the maximum displacement set. To resort to a more general expression for the phenomenon under study, the experimental results were thoroughly analysed: it was found that the dependence of both the constants on the displacement can be modelled by simple linear relationships. By this finding, the fatigue data pertaining to all the fatigue conditions adopted could be reduced to a single master curve.

Controlled states of damage were imparted to carbon fibre reinforced plastic panels by simply supporting them on a circular ring and applying a quasi-statically increasing transverse load at the centre. The damage state was controlled by interrupting the loading stage at predetermined values of the deflection. After mechanical tests, the panels were non-destructively inspected by a highly sensitive superconductive magnetometer (HTS-SQUID), from which maps of the parallel component of the magnetic field above the sample surface were obtained. A destructive analysis of the specimens was also carried out by optical microscopy, to assess damage features. The existence of a defect in the material was clearly signalled by a distortion in the magnetic field, even when an elastic behaviour could be guessed from the load–displacement curve. During loading conditions, which only resulted in failures in the matrix, the slope of the SQUID response along a line-scan was linearly dependent on the maximum energy applied to the specimen during the mechanical tests. The dependence of the slope on the energy was strongly altered when fibre failures were induced in the laminate. The magnetometer response was also influenced by the coil excitation frequency. The results obtained at different frequencies indicate that the optimum frequency can vary, depending on the scope of the non-destructive inspection under concern.

An experimental investigation was carried out, in order to find simple analytical methods for the prediction of pin-bearing strength of glass mat reinforced plastics fabricated by hand lay-up. The specimens tested exhibited different failure modes, consisting of net-tension, cleavage, and bearing, depending on the geometry adopted. The parameters affecting the bearing strength were the ratio of the specimen width to the hole diameter D, and the ratio of the edge distance to D. The maximum bearing strength was attained when a pure bearing failure happened. The latter was the only safe failure mode: after its occurrence, the joint was still able to support about 70% of its virgin strength. The experimental data obtained were used to assess a simple procedure for the calculation of the joint load carrying capacity, previously proposed. Since a large scatter was found in the bearing strength of the material, the data were analysed statistically, assuming a probability of failure varying according to a two-parameter Weibull distribution. An excellent agreement was found between the experimental results and the theoretical model. Similar conclusions were drawn applying the previous approach to the residual strength after bearing failure. A limited amount of tests was performed to verify the influence of possible damage induced during hole drilling on the bearing behaviour. It was found that a 20% decrease in bearing strength occurs when delamination is induced by inaccurate drilling. However, the residual bearing strength was substantially unaffected by the drilling damage.

The paper deals with the prediction of penetration energy of fibre reinforced plastics subjected to low-velocity impact. Some results available in the literature are reviewed first, allowing to individuate the main parameters affecting the energy absorbing capacity of a composite laminate. It is shown that, for a given fibre type, the penetration energy is substantially influenced by the total fibre volume and tup diameter, whereas other factors, such as resin type and content, fibre architecture, stacking sequence and orientations, play a secondary role in the phenomenon. Then, an empirical power law equation recently proposed by the authors, from which the penetration energy can be evaluated, is assessed on the basis of experimental data previously published. The results indicate that the exponent of the power law is perhaps independent of the material considered, being practically the same for graphite fibre, as well as glass fibre reinforced plastics, and even for an isotropic material as polycarbonate, prone to extensive plastic yielding before final failure. The formula proposed, useful for in-plane isotropic and moderately anisotropic composites, can also permit the comparison of impact data generated under different impact conditions.

A recent two-parameter model, successfully employed to predict the flexural fatigue lifetime of randomly oriented glass fibre reinforced plastics, is applied to experimental data available in the literature, concerning carbon fibre reinforced plastic-laminates subjected to tension-tension fatigue. It is shown that the model accurately reproduces not only the classical S-N curve, but also the probability of failure under assigned loading conditions, if its constants are calculated by a minimum number of experimental tests. However, the results also demonstrated that the proposed method fails in describing the residual strength decay with cycle evolution, resulting in very conservative estimates. This was unexpected, because the formula for fatigue life directly derives from a precise assumption on the law governing the strength degradation. From the results presented, it is concluded that the model must be considered as an empirical formula, yet efficient in predicting fatigue life.

A sandwich beam loaded in three-point bending (TPB) was employed for the shear characterization of foam cores destined to structural sandwich application. In the design of the specimen, particular care was taken to avoid measurement errors deriving from the flexural component of the displacement and from the de Saint Venant's effects, yet retaining the simplicity in the formulae for data reduction. Using the new method, experimental tests were carried out on a PVC foam 55 Kg/M3 in density. For comparison, shear characterization tests were also performed according to ISO 1922. The results obtained demonstrate that, when the core shear modulus is considered, TPB and ISO 1922 can provide practically coincident results. However, TPB yielded a shear strength about 20% higher than the ISO Standard, together with a shear strain at failure that is 10% lower. The failure modes observed suggest that the core shear behavior is better represented by TPB, whereas ISO 1922 is unsuitable to correctly measure the core shear strength.

Monotonic and fatigue tests were carried out in four-point bending on a glass fabric/epoxy composite, using two different stress ratios. Ultimate failure both in monotonic tests and in fatigue was precipitated by microbuckling phenomena happening at the compression side of the specimens. The experimental results were evaluated adopting a fatigue model statistically implemented, based on the hypothesis of a two-parameter Weibull distribution of the monotonic strength, previously assessed for random glass fibre reinforced plastics failed in tension. The fatigue model was able to account for the effect of the stress ratio on the fatigue life, accurately predicting the classical S–N curve. By the model, the virgin strength for each specimen failed in fatigue was evaluated, and the distributions of the measured and calculated monotonic strength were compared. Some discrepancies between the two distributions, resulting in poor agreement in the tail portions of the curves, were noted. It is shown that the inconsistencies found are probably attributable to the inadequancy of a two-parameter Weibull curve to describe the actual material trend. Better results were obtained by using a three-parameter Weibull distribution.

Glass-forming materials, including thermosetting and thermoplastic resins commonly used in polymer-matrix composites for high-performance applications, undergo structural relaxation when they are cooled through the glass transition region owing to the glassy non-equilibrium state. The process of moving towards equilibrium consists essentially of a densification of the matter and follows complex paths deriving from its inherent non-linear and non-exponential character. The structural relaxation is observable in a laboratory time-scale at temperatures below but close to T g , and is related to the durability of polymeric materials because it is characterized by changes of structure-sensitive properties until equilibrium is approached. Polymer-based composites suffer the same shortcoming even if the properties are fiber-dominated. In this paper sub- T g annealing studies have been carried out with both plain PEI and its carbon-fiber composites in order to observe the kinetics of structural relaxation. The experimental technique used is differential scanning calorimetry (DSC), which measures the enthalpy recovery during the structural relaxation. The investigation regarding the plain resin consisted of aging treatments at T g −10°C, T g −20°C and T g −30°C, for different annealing times ranging between 0 and 168 h. The experimental data were used to calculate the parameters of a long-term predictive model for the enthalpy relaxation based on the Narayanaswamy approach. The structural relaxation of the in situ resin (i.e. the resin constrained into the fibers lattice) was also investigated at T g −20°C taking into account the marked decrease of the glass transition temperature resulting from the overall manufacturing process. The comparison between the plain and the in situ matrix was done on the basis of the same degree of undercooling (i.e. the same distance from T g ). It was found that the composite aged faster than the plain matrix. The macroscopic effects of structural relaxation on PEI based composites were analyzed by fatigue tests in four-point bending geometry at different level of stress ratio R (the ratio of the minimum to the maximum stress). The aged samples showed a higher characteristic strength, which resulted in a correspondingly higher fatigue life compared to the as manufactured materials.

Orthogonal cutting tests were carried out on unidirectional glass-fibre-reinforced plastics, using high-speed steel tools. During the tests, the tool rake and relief angle, and the depth of cut t were varied, whereas the cutting direction was held parallel to the fibre orientation. The trend of the principal forces recorded during cutting clearly showed the so-called `size effect': the unit cutting force (also known as `specific energy') was a decreasing function of the depth of cut, tending to infinity for vanishingly small values of t. A previous force scheme, assuming a significant influence of the friction generated by the work material sliding along the tool flank on the overall cutting forces, was utilized to interpret the cutting data, and to differently define the unit cutting force. According to the model, the unit cutting force and the coefficient of friction were independent of both the relief angle and the depth of cut, although the former, as expected, sensibly decreased with increasing the rake angle.

A particular class of composite laminates is presented, where coupling ef fects are rigorously zero.