A progressive failure model for composite laminates subjected to low velocity impact damage

This paper presents a 3-D failure model for predicting the dynamic material response of composite laminates under impact loading. The formulation is based on the Continuum Damage Mechanics (CDM) approach and enables the control of the energy dissipation associated with each failure mode regardless of mesh refinement and fracture plane orientation. Internal thermodynamically irreversible damage variables were defined in order to quantify damage concentration associated with each possible failure mode and predict the gradual stiffness reduction during the impact damage process. The material model has been implemented into LS-DYNA explicit finite element code within solid elements and it has proven to be capable of reproducing experimental results with good accuracy in terms of static/dynamic responses, absorbed energy and extent of damage.

A pseudo-transient solution strategy for the analysis of delamination by means of interface elements

Recent efforts in the finite element modelling of delamination have concentrated on the development of cohesive interface elements. These are characterised by a bilinear constitutive law, where there is an initial high positive stiffness until a threshold stress level is reached, followed by a negative tangent stiffness representing softening (or damage evolution). Complete decohesion occurs when the amount of work done per unit area of crack surface is equal to a critical strain energy release rate. It is difficult to achieve a stable, oscillation-free solution beyond the onset of damage, using standard implicit quasi-static methods, unless a very refined mesh is used. In the present paper, a new solution strategy is proposed based on a pseudo-transient formulation and demonstrated through the modelling of a double cantilever beam undergoing Mode I delamination. A detailed analysis into the sensitivity of the user-defined parameters is also presented. Comparisons with other published solutions using a quasi-static formulation show that the pseudo-transient formulation gives improved accuracy and oscillation-free results with coarser meshes

Delamination threshold load for dynamic impact on plates

A criterion is derived for delamination onset in transversely isotropic laminated plates under small mass, high velocity impact. The resulting delamination threshold load is about 21% higher than the corresponding quasi-static threshold load. A closed form approximation for the peak impact load is then used to predict the delamination threshold velocity. The theory is validated for a range of test cases by comparison with 3D finite element simulation using LS-DYNA and a newly developed interface element to model delamination onset and growth. The predicted delamination threshold loads and velocities are in very good agreement with the finite element simulations. Good agreement is also shown in a comparison with published experimental results. In contrast to quasi-static impacts, delamination growth occurs under a rapidly decreasing load. Inclusion of finite thickness effects and a proper description of the contact stiffness are found to be vital for accurate prediction of the delamination threshold velocity

Development of calcium phosphate cement for the augmentation of traumatically fractured porcine specimens using vertebroplasty

The study aim was to develop and apply an experimental technique to determine the biomechanical effect of polymethylmethacrylate (PMMA) and calcium phosphate (CaP) cement on the stiffness and strength of augmented vertebrae following traumatic fracture. Twelve burst type fractures were generated in porcine three-vertebra segments. The specimens were randomly split into two groups (n=6), imaged using microCT and tested under axial loading. The two groups of fractured specimens underwent a vertebroplasty procedure, one group was augmented with CaP cement designed and developed at Queen's University Belfast. The other group was augmented with PMMA cement (WHW Plastics, Hull, UK). The specimens were imaged and re-tested . An intact single vertebra specimen group (n=12) was also imaged and tested under axial loading. A significant decrease (p<0.01) was found between the stiffness of the fractured and intact groups, demonstrating that the fractures generated were sufficiently severe, to adversely affect mechanical behaviour. Significant increase (p<0.01) in failure load was found for the specimen group augmented with the PMMA cement compared to the pre-augmentation group, conversely, no significant increase (p<0.01) was found in the failure load of the specimens augmented with CaP cement, this is attributed to the significantly (p<0.05) lower volume of CaP cement that was successfully injected into the fracture, compared to the PMMA cement. The effect of the percentage of cement fracture fill, cement modulus on the specimen stiffness and ultimate failure load could be investigated further by using the methods developed within this study to test a more injectable CaP cement.

An investigation into the acceleration response of a damaged beam-type structure to a moving force

In recent years there have been a growing number of publications on procedures for damage detection in beams from analysing their dynamic response to the passage of a moving force. Most of this research demonstrates their effectiveness by showing that a singularity that did not appear in the healthy structure is present in the response of the damaged structure. This paper elucidates from first principles how the acceleration response can be assumed to consist of ‘static’ and ‘dynamic’ components, and where the beam has experienced a localised loss in stiffness, an additional ‘damage’ component. The combination of these components establishes how the damage singularity will appear in the total response. For a given damage severity, the amplitude of the ‘damage’ component will depend on how close the damage location is to the sensor, and its frequency content will increase with higher velocities of the moving force. The latter has implications for damage detection because if the frequency content of the ‘damage’ component includes bridge and/or vehicle frequencies, it becomes more difficult to identify damage. The paper illustrates how a thorough understanding of the relationship between the ‘static‘ and ‘damage’ components contributes to establish if damage has occurred and to provide an estimation of its location and severity. The findings are corroborated using accelerations from a planar finite element simulation model where the effects of force velocity and bridge span are examined.

Effects of confining pressure and water content on performance of unsaturated compacted clay under repeated loading

This paper examines the performance of unsaturated soils under repeated loading. As part of the research, a triaxial system was developed that incorporates small-strain measurements using Hall effect transducers, in addition to suction measurements taken using a psychrometer. Tests were conducted on samples of kaolin under constant water mass conditions. The results address the effects of compaction effort and water content at the time of compaction on the overall performance of unsaturated soils, under different amplitudes of loading and different confining pressures. The results show that suction in the sample reduced with increasing number of loading cycles of the same magnitude. The resilient modulus initially increased with increasing water content up to approximately optimum water content, and then reduced substantially with further increase in water content.

Fatigue Life Assessment and Static Testing of Structural GFRP Tubes Based on Coupon Tests

Fiber-reinforced polymer (FRP) hollow tubes are used in structural applications, such as utility poles and pipelines. Concrete-filled FRP tubes (CFFTs) are also used as piles and bridge piers. Applications such as poles and marine piles are typically governed by cyclic bending. In this paper, the fatigue behavior of glass-FRP filament-wound tubes is studied using coupons cut from the tubes. Several coupon configurations were first examined in 24 tension and five compression monotonic loading tests. Fatigue tests were then conducted on 81 coupons to examine several parameters; namely, loading frequency as well as maximum-to-ultimate (max ult) and minimum-to-maximum (min max) stress ratios, including tension tension and tension compression, to simulate reversed bending. The study demonstrated the sensitivity of test results and failure mode to coupon configuration. The presence of compression loads reduced fatigue life, while increasing load frequency increased fatigue life. Stiffness degradation behavior was also established. To achieve at least one million cycles, it is recommended to limit (max ult) to 0.25. Models were used to simulate stiffness degradation and fatigue life curve of the tube. Fatigue life predictions of large CFFT beams showed good correlation with experimental results. © 2008 ASCE.

An experimental and numerical investigation into the seismic performance of a multi-storey concentrically braced plan irregular structure

In this investigation, the seismic torsional response of a multi-storey concentrically braced frame (CBF) plan irregular structure is evaluated numerically and experimentally through a series of hybrid tests. CBF structures have become popular in seismic design because they are one of the most efficient types of steel structures to resist earthquake loading. However, their response under plan irregular conditions has received little focus mostly in part
due to their complex behaviour under seismic loading conditions. The majority of research on the seismic response of plan irregular structures is based purely on numerical investigations. This paper provides much needed experimental investigation of the seismic response of a CBF plan irregular structure with the aim of characterising the response of this class of structure. The effectiveness of the Eurocode 8 torsional effects provision as a method of designing for
low levels of mass eccentricity is evaluated. Results indicate that some of the observations made by purely numerical models are valid in that; torsionally stiff structures perform well and the stiff side of the structure is subjected to a greater ductility demand compared to the flexible side of the structure. The Eurocode 8 torsional effects provision is shown to be adequate in terms of ductility and interstorey drift however the structure performs poorly
in terms of floor rotation. Importantly, stiffness eccentricity occurs when the provision is applied to the structure when no mass eccentricity exists and results in a significant increase in floor rotations.

A laboratory based model study. Experimental observations of footings supported on soft clay reinforced with granular columns.

The inclusion of granular columns in soft clay deposits leads to improvements in bearing capacity and overall stiffness along with a reduction in consolidation settlement. Many laboratory investigations have focused on aspects of bearing capacity, but published data on settlement performance is limited. This paper reports on some interesting findings obtained from a laboratory model study in respect of these issues. In this investigation, 300 mm diameter by 400 mm long samples of soft kaolin clay were reinforced with single or multiple granular columns of various lengths using the displacement and replacement installation methods. The experimental findings revealed that, for the same area replacement ratio, limited settlement reduction was achieved for single long floating columns and end-bearing column groups. Marginal improvements in settlement performance were also achieved for columns installed by the displacement method. No settlement reduction was achieved for short single floating columns while short floating granular column groups produced increased settlements. These observations were verified using contact pressure measurements between the footing and column/surrounding clay.

Biomechanics of Vertebroplasty: Effect of Cement Viscosity on Mechanical Behaviour

Vertebroplasty is a minimally invasive surgical procedure, which requires efficacious percutaneous cement delivery via a cannulated needle to restore the strength and stiffness in osteoporotic vertebral bodies. Cement viscosity is understood to influence the injectability, cohesion and cement retention within the vertebral body. Altering the liquid to powder ratio modifies the viscosity of bone cement; however, the cement viscosity-response association between cement fill and augmentation of strength and stiffness is unknown. The aim of this study was to determine the relationship between viscosity, cement fill and the potential augmentation of strength and stiffness in an open pore foam structure that was representative of osteoporotic cancellous bone using an in vitro prophylactic vertebroplasty model. The results showed a strong linear correlation between compressive strength and stiffness augmentation with percentage cement fill, the extent of which was strongly dependent on the cement viscosity. Significant forces were required to ensure maximum delivery of the high viscosity cement using a proprietary screw-driven cement delivery technology. These forces could potentially exceed the normal human physical limit. Similar trends were observed when comparing the results from this study and previously reported cadaveric and animal based in vitro models.

Influence of test methodology and probe geometry on nanoscale fatigue mechanisms of diamond-like carbon thin film

The aim of this paper is to investigate the mechanism of nanoscale fatigue using nano-impact and multiple-loading cycle nanoindentation tests, and compare it to previously reported findings of nanoscale fatigue using integrated stiffness and depth sensing approach. Two different film loading mechanism, loading history and indenter shapes are compared to comprehend the influence of test methodology on the nanoscale fatigue failure mechanisms of DLC film. An amorphous 100 nm thick DLC film was deposited on a 500 μm silicon substrate using sputtering of graphite target in pure argon atmosphere. Nano-impact and multiple-load cycle indentations were performed in the load range of 100 μN to 1000 μN and 0.1 mN to 100 mN, respectively. Both test types were conducted using conical and Berkovich indenters. Results indicate that for the case of conical indenter, the combination of nano-impact and multiple-loading cycle nanoindentation tests provide information on the life and failure mechanism of DLC film, which is comparable to the previously reported findings using the integrated stiffness and depth sensing approach. However, the comparison of results is sensitive to the applied load, loading mechanism, test-type and probe geometry. The loading mechanism and load history is therefore critical which also leads to two different definitions of film failure. The choice of exact test methodology, load and probe geometry should therefore be dictated by the in-service tribological conditions, and where necessary both test methodologies can be used to provide better insights of failure mechanism. Molecular dynamics (MD) simulations of the elastic response of nanoindentation is reported, which indicates that the elastic modulus of the film measured using MD simulation was higher than that experimentally measured. This difference is attributed to the factors related to the presence of material defects, crystal structure, residual stress, indenter geometry and loading/unloading rate differences between the MD and experimental results.

Multibody modelling of a TB31 and a TB32 crash test with vertical portable concrete barriers: model verification and sensitivity analysis.

In this article the multibody simulation software package MADYMO for analysing and optimizing occupant safety design was used to model crash tests for Normal Containment barriers in accordance with EN 1317. The verification process was carried out by simulating a TB31 and a TB32 crash test performed on vertical portable concrete barriers and by comparing the numerical results to those obtained experimentally. The same modelling approach was applied to both tests to evaluate the predictive capacity of the modelling at two different impact speeds. A sensitivity analysis of the vehicle stiffness was also carried out. The capacity to predict all of the principal EN1317 criteria was assessed for the first time: the acceleration severity index, the theoretical head impact velocity, the barrier working width and the vehicle exit box. Results showed a maximum error of 6% for the acceleration severity index and 21% for theoretical head impact velocity for the numerical simulation in comparison to the recorded data. The exit box position was predicted with a maximum error of 4°. For the working width, a large percentage difference was observed for test TB31 due to the small absolute value of the barrier deflection but the results were well within the limit value from the standard for both tests. The sensitivity analysis showed the robustness of the modelling with respect to contact stiffness increase of ±20% and ±40%. This is the first multibody model of portable concrete barriers that can reproduce not only the acceleration severity index but all the test criteria of EN 1317 and is therefore a valuable tool for new product development and for injury biomechanics research.

Integrating allowable design strains in composites with whole life value

Fibre-Reinforced Plastics (FRPs) have been used in civil aerospace vehicles for decades. The current state-of-the-art in airframe design and manufacture results in approximately half the airframe mass attributable to FRP materials. The continual increase in the use of FRP materials over metallic alloys is attributable to the material's superior specific strength and stiffness, fatigue performance and corrosion resistance. However, the full potential of these materials has yet to be exploited as analysis methods to predict physical failure with equal accuracy and robustness are not yet available. The result is a conservative approach to design, but one that can bring benefit via increased inspection intervals and reduced cost over the vehicle life. The challenge is that the methods used in practice are based on empirical tests and real relationships and drivers are difficult to see in this complex process and so the trade-off decision is challenging and uncertain. The aim of this feasibility study was to scope a viable process which could help develop some rules and relationships based on the fundamental mechanics of composite material and the economics of production and operation, which would enhance understanding of the role and impact of design allowables across the life of a composite structure.

Micro-mechanical analysis of bonding failure in a particle-filled composite

Composites with a weak interface between the filler and matrix which are susceptible to interfacial crack formation are studied. A finite-element model is developed to predict the stres/strain behavior of particulate composites with an interfacial crack. This condition can be distinguished as a partially bonded inclusion. Another case arises when there is no bonding between the inclusion and the matrix. In this latter case the slip boundary condition is imposed on the section of the interface which remains closed. The states of stress and displacement fields are obtained for both cases. The location of any further deformation through crazing or shear band formation is identified as the crack tip. A completely unbonded inclusion with partial slip at a section of the interface reduces the concentration of the stress at the crack tip. Whereas this might lead to slightly higher strength, it decreases the load-transfer efficiency and stiffness of this type of composite. © 2002 Elsevier Science Ltd. All rights reserved.

Morphology and compression behaviour of biodegradable scaffolds produced by the sintering process

Porous poly(L-lactic acid) (PLA) scaffolds of 85 per cent and 90 per cent porosity are prepared using polymer sintering and porogen leaching method. Different weight fractions of 10 per cent, 30 per cent, and 50 per cent of hydroxyapatite (HA) are added to the PLA to control the acidity and degradation rate. The three-dimensional (3D) morphology and surface porosity are tested using micro-computer tomography (micro-CT), optical microscopy, and scanning electron microscopy (SEM). Results indicate that the surface porosity does not change on the addition of HA. The micro-CT examinations show a slight decrease in the pore size and increase in the wall thickness accompanied by reduced anisotropy for the scaffolds containing HA. Scanning electron micrographs show detectable interconnected pores for the scaffold with pure PLA. Addition of the HA results in agglomeration of the HA particles and reduced leaching of the porogen. Compression tests of the scaffold identify three stages in the stress-strain curve. The addition of HA results in a reduction in the modulus of the scaffold at the first stage of elastic bending of the wall, but this is reversed for the second and third stages of collapse of the wall and densification in the compression tests. In the scaffolds with 85 per cent porosity, the addition of a high percentage of HA could result in 70 per cent decrease in stiffness in the first stage, 200 per cent increase in stiffness in the second stage, and 20 per cent increase in stiffness in the third stage. The results of these tests are compared with the Gibson cellular material model that is proposed for prediction of the behaviour of cellular material under compression. The pH and molecular weight changes are tracked for the scaffolds within a period of 35 days. The addition of HA keeps the pH in the alkaline region, which results in higher rate of degradation at an early period of observation, followed by a reduced rate of degradation later in the process. The final molecular weight is higher for the scaffolds with HA than for scaffolds of pure PLA. The manufactured scaffolds offer acceptable properties in terms of the pore size range and interconnectivity of the pores and porosity for non-load-bearing bone graft substitute; however, improvement to the mixing of the phases of PLA and HA is required to achieve better integrity of the composite scaffolds. © 2008 IMechE.