Single Cantilever Beam Research Articles

Virtual crack closure technique in peridynamic theory

In this paper, the virtual crack closure technique (VCCT), commonly used in the numerical finite element method (FEM), is for the first time reformulated in nonlocal peridynamic theory, and a new peridynamics-based virtual crack closure technique (PD_VCCT) is proposed for the energy release rate calculation in the framework of peridynamics. The mode I, mode II, and their mixed mode fracture cases are considered. Two typical tests using the single edge-notched tension (SENT) and asymmetric double cantilever beams (ADCB) specimens are considered for implementation and verification, and the numerical energy release rates calculated by the present PD_VCCT are compared with those by the FEM-based VCCT. The close comparisons demonstrate that the proposed PD_VCCT can successfully predict the energy release rates for the cases of mode I, mode II and their mixed mode fracture and it can be used as a viable and effective tool for fracture analysis.

Fabrication and investigation on damping performance of novel co‐curing sandwich composites

AbstractA new kind of co‐cured sandwich composite was manufactured via inserting tailored damping materials between the lamina to enhance vibration characteristics and sound insulation performance of traditional sandwich composite. The sandwich material was investigated based on the theory of co‐curing, which was superior to the preparation process of traditional sandwich composite. The viscous flow characteristics of epoxy resin and rubber sandwich were considered in the preparation process. The damping characteristics and sound insulation properties of the sandwich composite were determined by the single cantilever beam vibration test and the standing wave tube method. The loss factor of the sandwich composites with damping layer thickness of 0.1 mm reaches 3.384%, which increases by 102.81% compared with that of the undamped composite. The experimental results reveal that the novel damping polymer enhances the damping characteristic and sound insulation performance of laminates significantly compared with previous sandwich composite. The conclusion indicates that the co‐cured composite structures show a strong ability of vibration reduction and sound insulation.

Collapse analysis of a large plastic pipe using cohesive zone modelling technique

Polypropylene (PP) plastic pipes have recently gained widespread application in non-pressurized gravity pipes used for seawater intake lines in the petrochemical industry. These pipes consist of a solid wall base pipe, on which an outer reinforcement called the omega-profile is spirally winded and hot fusion bonded. The omega-profile is usually filled with grout to provide on-bottom stability for subsea installation. It is of high importance that the bond between the omega-profile and the base pipe has sufficient strength to provide resistance against buckling of the pipeline system. The objective of this study is to investigate the collapse behaviour of such large-diameter PP pipes subjected to a negative internal pressure. The bond is modelled with cohesive zone modelling technique with the aim to determine the failure mode that governs the collapse behaviour of the pipe, e.g. buckling or delamination. Experiments where conducted on single cantilever beam (SCB) specimens cut from the pipe to determine the cohesive bond strength between the omega-profile and base pipe. The findings from the experiments are implemented in a full pipe model, where the surface between the omega-profile and base pipe is assigned bond strength characteristics in accordance with the experimental results. The FEA results of the non-linear collapse analysis of the full pipe model show that for the range of grout stiffness values considered (0 ≤ Eg ≤ 30 GPa), the governing failure mode of the pipe is initiated by buckling and proceeded by delamination. For delamination to govern the failure mode, a grout stiffness greater than 36 GPa in combination with a weaker bond strength than the experimentally measured would be required. The methodology presented in this study gives a rather accurate tool for the design and analysis of this type of structures, and can reliably assess the bond strength level required in view of the governing failure modes, e.g. buckling and delamination.

Crack length correction and root rotation angle in a sandwich single cantilever beam (SCB) fracture specimen

Crack root rotation is a measure of deviation from clamped boundary conditions of region in front of the crack tip. The root rotation depends on the shear force and bending moment acting at the crack tip. Such rotation significantly affects the compliance and energy-release rate. Crack root rotation analysis of Single Cantilever Beam (SCB) sandwich specimens is presented here. Closed-form solutions for the root rotation angle obtained from the foundation analysis are compared to finite element analysis (FEA) predictions. The derived expressions closely match for a range of sandwich configurations. An expression for the energy-release rate, derived from the foundation analysis was found to agree with FEA predictions over a large range of face-to-core modulus ratios. Energy-release rate and mode mixity phase angle increased with decreasing crack length due to the transverse shear effects. At longer crack lengths, both energy-release rate and phase angle reached a value independent of crack length. The foundation model is used to derive a simple expression for the offset crack length for the SCB sandwich fracture test. It is shown that the obtained formulation agrees closely well with both numerical and experimental values. In addition, SCB fracture tests performed using an in-house built translatable rig showed close relation to both analytical and numerical compliance results.

Closed form solution for the energy release rate and mode partitioning of the single cantilever beam sandwich debond from an elastic foundation analysis

The goal of this paper is to derive closed form expressions for the energy release rate and mode partitioning offace/core debonds for the Single Cantilever Beam Sandwich Composite testing configuration, which is loaded with an applied shear force and/or bending moment. This is achieved by an elastic foundation approach, in which a finite length sandwich beam is treated as having a free “debonded” section and a “joined” section where a series of springs exists between the face and the substrate (core and bottom face). The elastic foundation analysis is done for a general asymmetric sandwich construction. A J-integral approach is subsequently used to derive a closed form expression for the energy release rate. It is also shown that the energy release rate is very close to the differential energy stored in the springs at the beginning of the elastic foundation, i.e. the energy released by the “broken” differential spring element as the debond propagates. In the context of this elastic foundation model, a mode partitioning measure is defined based on the transverse and axial displacements at the beginning of the elastic foundation. Since the normal springs account for the transverse compressibility of the core but not for the shear, a correction for the shear of the substrate is included by deriving the expression for the corresponding shear angle and accounting for the additional horizontal “tip” displacement. The results are compared with finite element results for a range of core materials and show very good agreement.

Characterizing photovoltaic backsheet adhesion degradation using the wedge and single cantilever beam tests, Part I: Field Modules

Photovoltaic backsheets are exposed to harsh outdoor weathering conditions throughout their service lives that can compromise their protective function, through adhesive debonding between their constituent layers and between the backsheet and the module. A large-scale study on adhesive degradation was conducted on 37 field-exposed modules, that spanned 19 different module manufacturers, that were deployed among six Köppen–Geiger climatic zones, and that were fielded between 0 and 28 years. Six outer layer polymer classes were identified among the backsheets: polyamide (PA), polyethylene terephthalate (PET), polyvinyl fluoride (PVF), polyvinylidene fluoride (PVDF), fluoroethylene vinyl ether copolymer (FEVE), and tetrafluoroethylene hexafluoropropylene vinylidene fluoride copolymer (THV). Two adhesion tests were used to measure the adhesive strength: the wedge test and the width-tapered single-cantilever beam (SCB) test. Adhesion energies were compared across exposure time and Köppen–Geiger climatic zone. Many of the PET-, PVF-, and PVDF-based backsheets experienced degradation of the adhesive layer between the backsheet outer and core layers. A consistent trend of decreasing adhesion energy with exposure time was observed in five out of the six backsheet types. Trends among adhesion energy and climatic zone, while expected, were not observed, possibly due to broad ranges in temperature, humidity, and precipitation defining Köppen–Geiger climatic zones. The cantilever beam measurements produced an upper cutoff of approximately 100 J/m2, above which no modules exhibited field delamination. The results are part of a two-part study quantifying adhesion in both field-weathered and indoor-exposed PV backsheets.

Damage initiation and fracture analysis of honeycomb core single cantilever beam sandwich specimens

Fracture testing and analysis of aerospace grade honeycomb core sandwich constructions using a single cantilever beam test methodology is presented here. Influence of various parameters such as facesheet thickness, core density, honeycomb cell-size, and core thickness were studied. A Winkler-based foundation model was used to calculate compliance and energy-release rate, and further compare with finite element model and experiments. A cohesive zone model was developed to predict the disbond initiation and simulate the interface crack propagation in the single cantilever beam sandwich specimen. The mode I interface fracture toughness obtained from the translating base single cantilever beam setup was provided as input in this cohesive zone model. It is shown that the presented cohesive zone approach is robust, and is able to capture the debonding phenomenon for majority of the honeycomb core specimens.

Characterizing photovoltaic backsheet adhesion degradation using the wedge and single cantilever beam tests, Part II: Accelerated tests

Photovoltaic (PV) backsheets provide critical moisture, mechanical, and electrical insulation to the backside of PV modules, but their continued functionality depends upon their ability to remain well adhered over years of harsh environmental exposure. A study of adhesive strength was conducted on several PV backsheet types exposed to indoor accelerated weathering. Two adhesion tests – the wedge test and single cantilever beam test – were used to measure adhesion energy in four backsheets: two with fluoropolymer-based outer (airside) layers – polyvinyl fluoride (PVF), polyvinylidene fluoride (PVDF) – and two with non-fluoropolymer-based outer layers–polyamide (PA) and polyethylene terephthalate (PET). The effects of changes in temperature, ultraviolet (UV) irradiance, relative humidity, and a periodic water spray were studied. The PET-, PVF- and PVDF-based backsheets all showed instances of debonding in an adhesive layer, which is commonly reported. For the PA-, PET-, and PVDF-based backsheets, adhesion energy dropped fairly rapidly with exposure, reaching very low levels by 4000 h. The PVF-based backsheet was relatively robust to weathering. Pull-off of an outer chalking layer in the PA- and PET-based backsheets suggested a sensitivity to UV. Adhesion in these two backsheets was also highly sensitive to changes in moisture level. Changes in UV irradiance and temperature did not show a statistically significant effect on adhesion loss for the exposure levels used. The present work is part of a two-part adhesion study on both field-weathered and indoor-exposed backsheets, and forms a basis for understanding adhesion degradation across a variety of backsheet types and degradation factors.

Interlaminar fracture toughness analysis of fiber reinforced metal laminates based on APDL

Fiber Reinforced Metal Laminates (FRMLs) are widely used in modern industry because of excellent comprehensive properties. However, due to the existence of the interface, there will be delamination damage in their use process. Interface is the weakest part of fiber reinforced metal laminates. The bonding strength at the interface is determined by the fracture toughness of the interface. It is an important mechanical property index of fiber reinforced metal laminates. It is usually measured by a single cantilever beam test. In this paper, the finite element model of fiber reinforced metal laminate was constructed based parametric design language APDL of ANSYS to simulate the fracture roughness tests of FRMLs using element birth-death technology. The results show that the numerical simulation is very close to the experimental results. The numerical simulation is a very effective method to determine the interlaminar fracture toughness of fiber reinforced metal laminates.

Effect of Including Cracked Core in a Beam on Elastic Foundation Analysis Model for Sandwich Single Cantilever Beam Test Specimen

Effect of Including Cracked Core in a Beam on Elastic Foundation Analysis Model for Sandwich Single Cantilever Beam Test Specimen

Residual Strain Predictions for a Powder Bed Fusion Inconel 625 Single Cantilever Part

The laser powder bed fusion (LPBF) process involves using a laser beam to selectively melt metal powder with a desired shape on a substrate to create a part layer-by-layer. As an Additive Manufacturing (AM) process, laser powder bed fusion (commonly referred to as selective laser melting—SLM) offers superior design freedom over conventional manufacturing methods and enables the production of complex, lightweight geometries with applications in the aerospace, automotive, and biomedical industries. In addition to enhanced design freedom, AM technologies provide improved material utilization and allow for reduced assembly needs. However, the reliability and repeatability of additively manufactured parts is a challenge to the wide-scale adoption of the technology for safety critical parts. A critical limitation of process optimization is the prediction and control of residual stresses, distortion, and microstructure evolution. This work focuses on the development and implementation of a numerical modeling technique for the prediction of residual strains within an Inconel 625 LPBF part. The model, using the SIMULIA Additive Manufacturing Scenario App, based on the Abaqus 2018 finite element solver, was developed and analyzed as part of a submission for the NIST AM Benchmark 2018. A sequentially coupled thermo-mechanical analysis was adopted to replicate the building conditions of a single cantilever beam built at the NIST laboratories. The results of the blind study were compared to X-ray diffraction (XRD) measurements of the physical build. The predicted three-dimensional residual strain field showed a high level of accuracy and the submission described in this paper received joint first prize in the residual elastic strain category of the NIST AM Benchmark 2018. The results presented in this paper reflect only findings before the benchmark measurements were posted on the NIST website.

Influence of geometry, elasticity properties and boundary conditions on the Mode I purity in sandwich composites

The present work addresses the problem of skin/core debonding in sandwich materials. The main goal is to carry out parametric analyses for studying the influence of various materials, geometrical parameters and boundary conditions of sandwich fracture specimens such as a Single Cantilever Beam and a Double Cantilever Beam on the skin/core opening (KI) and shearing (KII) modes. The analyses have been performed by means of fracture mechanics tools implemented into the commercial finite element code ABAQUSTM. A two-dimensional model of the fracture specimens has been developed with plane strain finite elements. The dependence of the stress intensity factors in the sandwich specimens on the skin thickness, ratio between the Young’s moduli of the skin and core materials and boundary conditions imposed on the specimens has been examined under quasi-static loading by using the interaction integral method.

When Stretchable Sensing Meet Flexible Robotics

Advantages of soft, flexible materials with developments in stretchable electronics can be intertwined for a promising sensorized flexible robotics platform to work on a resilient, adaptable manipulator aimed to meet ever-increasing demands in safe regulated medical environments. Taking advantages of these soft magnetic polymers, we propose a novel, soft-squishy and flexible bend sensor by determining the relationship between inductance changes with bending angle. This bend sensor employs flexible wire embedded in a silicone elastomer with the different permeable core. The principle notion is to have a comprehensive analysis of the change in morphology of the sensor with bending angle which can be translated to inductance generated therein. The performance of the sensor is evaluated with various experimental trials while analytical modeling elucidates that the bend angle is linearly proportional to the sensor signal citing R-square value up to 0.9204. The proposed sensor produces the desired output in the electromagnetic frequency range of 8-10 MHz with a tunable sensitivity of 0.418 mV/rad. The sensor is robust enough to stretch up to twice of its original length. The main advantage of this bend sensor is its simple fabrication technique, flexibility, robustness, and economical. Conclusively, this induction based tactile bending sensor is proved to produce robust output and can be extrapolated to sense bending angle using induction principle for the rehabilitative device, wearable robots, and related biomedical applications requiring low cost, soft and flexible operations. To equip robotic manipulators with intelligence, tactile sensors are extensively used for detecting various external stimuli like slippage, grasping force and imitate the tactile perceptions. Since past few decades, there have been various researches in realising sensing element on a soft surface to obtain stretchable, foldable and flexible sensors. Apart from these external stimuli measurements, various bend sensors were developed to determine the curvature of bending and utilized in different applications like measurements of flexion and extension of body joints. These bend sensors were realised on different hardware and software technology namely optical fibre bend sensor, resistive and capacitive-based sensor. For small size, increased MEMS sensors were developed. Resistive based sensors consist of pressure sensitive element which changes its resistance based on force or induced deformation. The sensitive element is usually comprised of conductive ink, rubber or elastomer. These sensors are affordable and commercially available in the market with a higher spatial resolution that employs fewer electronics which makes signal processing easier to work in mesh configurations. Apart from these above-mentioned technologies, inductive based tactile sensors are based on the principle of magnetic coupling. Modulating the inductance of the coil by varying the length and the permeable core, in turn, modulates the sensing voltage. The sensors based on this technology are still under development and not widely explored like others. Although they do not fix all the disadvantages of the above-mentioned technologies, they have a high dynamic range, linear output and can be employed at a higher frequency. This makes the construction bulky and incurs higher losses. Therefore, we aimed to develop a sensor with only one coil that acts as both primary and secondary/sensing coil. Specifically, we propose a novel soft inductive Solenoidal Bend Sensor (SBS) completely different from the existing technology. This sensor comprises of a flexible coil with a protective covering made of elastic material. This silicone elastomer provides mechanical compliance and robustness to the sensor. Due to SBS flexible yet resilient properties, this has promising applications in the field of wearable electronics, soft robotics, drug delivery, medical implants, human-machine interaction. In this paper, the geometry of the sensor is considered like a single cantilever beam hung through certain height and bent with tangential and normal force. Thus, the characterization and mathematical modelling of the sensor is simpler due to the simpler geometrical structure. This developed sensor uses a passive L–R circuitry that consists of a fixed resistor and a variable inductor. The variable inductor is coupled with elastomer element that makes dimensional changes in response to the target parameter to modify the inductance. The material and the design of the sensor is economical, readily available and does not require complex fabrication procedure. SBS can be modified by varying the wire gauge length. This novel SBS is sensitive to bidirectional force and can be calibrated in near terms for the measurement of the angle or the force in the finger joints for rehabilitation.

Fabrication of capacitive pressure sensor using single crystal diamond cantilever beam

Fabrication of single crystal diamond capacitive pressure sensor is presented. Firstly, the single crystal diamond cantilever beam was formed on HPHT diamond substrate by using selective high-energy ion implantation, metal patterning, ICP etching and electrochemical etching techniques. Secondly, on this diamond cantilever beam, the desired electrode patterns were processed with photolithography and metal evaporation methods. Furthermore, the displacements of cantilever beam under different pressure conditions were investigated by atomic force microscopy. The capacitance-voltage curves of single crystal diamond cantilever beam and substrate under different force loading conditions were measured by using Agilent B1505A parameter analyzer. The results show that sensitivity increases with the enlargement of electrode area of cantilever beam, and decreases with the rise of measurement frequency.

Preparation and damping properties of medium-temperature co-cured phenolic resin matrix composite structures

The structural damping composite was prepared by interleaving viscoelastic materials between the glass fiber reinforced phenolic resin laminates. It is different from the co-cured damping composites which have been investigated. Based on the principle of polymer synthesis, considering the curing process of resin and the vulcanization characteristics of damping material, the viscoelastic damping material was developed by orthogonal test method. The neutral layer was fabricated with damping film by brushing process. The damping properties of composite structures were researched by single cantilever beam vibration test. The variation curve of loss factor with respect to the thickness of damping layer was obtained. When the thickness of damping layer is 0.4 mm, the loss factor reaches a maximum. However, as the thickness of the damping layer augments, the growth rate of loss factor declines. Microscopic analysis of interlaminar fracture interface demonstrates that phenolic resin has excellent compatibility with viscoelastic damping materials.

Environmental Influence on Module Delamination Rate

This study begins to investigate the role of environmental factors, such as temperature and humidity, on the delamination kinetics of the ethylene vinyl acetate (EVA)/silicon–photovoltaic (Si–PV) cell interface. A fracture mechanics approach based on a single cantilever beam technique is employed to measure the delamination rate as a function of applied driving force. To glean insight into the mechanisms of bonding and degradation at this interface, and the effect of manufacturing variability and quality, we consider a high-quality pristine EVA and two EVAs formulated with reduced amounts of its adhesion promoter, silane. Results indicate that a bulk change in the viscoelastic properties of the EVA dominates the delamination kinetics at high driving forces and low humidity and the effect of a chemical reaction only becomes apparent at higher humidity and lower driving forces. These findings suggest that only interfacial phenomenon of susceptible, degraded material may have to be considered to adequately model PV module delamination failure.

The fracture behavior of sandwich composites with different core densities and thickness subjected to mode I loading at different temperatures

This study investigates the fracture behavior of the marine sandwich composite with a PVC foam core and face sheets of the glass fibre reinforced polymer fabricated by vacuum assisted resin infusion method. The strain energy release rate GI values (SERR) was obtained by analytical and experimental methods. For testing mode I, Single Cantilever Beam (SCB) test configuration was distinguished in order to prevent crack kinking. The special test apparatus was designed and manufactured for this experimental study. The effects of core density and core thickness on the fracture behavior of the sandwich composites at different temperatures were examined. The effects of four different temperatures (0, 23, 40 and 60 °C) on two core densities (80 and 130 kg m−3) and three core thickness (15, 20 and 25 mm) were studied under the fracture behavior concept. Finite element model was used for modeling the structure. ANSYS 15 was utilized to simulate mode I delamination and mechanical properties of face sheets and PVC foam obtained experimentally were used in the model. The SERR value was calculated using the virtual crack closure technique (VCCT). Reasonably good results were obtained between analytical and numerical methods.

Analysis of angular position, dimension and material of a cantilever piezoelectric energy harvester

The performance of an angular vibrating single piezoelectric cantilever beam energy harvester in a flexural mode was analyzed. In this research the approaches of theory, finite element, and experiment have been undertaken to study the effects of angular position, mechanical properties, and dimensions on the output power and resonance frequency of a piezoelectric cantilever beam. The phase shift is an important phenomenon observed in this system because of the angular position of the beam about its longitudinal axis. Frequency shift due to the angular position is usually observed in experiments. However, it has not been studied theoretically until now. The angular position not only affects the resonance frequency but also the amount of output power from the lead zirconate titanate ceramic bonded on it. Furthermore, beam and piezoelectric dimensions have a major effect on power output and resonance frequency. Another aspect considered in this research is the effect of materials on power and frequency which have been studied for aluminum, copper, and steel.

Numerical fracture analysis and model validation for disbonded honeycomb core sandwich composites

Disbond damage propagation in honeycomb core sandwich structures is investigated numerically and experimentally. A fully parametric two-dimensional finite element model of a disbonded honeycomb core sandwich specimen is presented. Energy release rate and mode-mixity were numerically determined using the Crack Surface Displacement Extrapolation (CSDE) method. An advanced method was adopted to obtain the homogenized mechanical properties of the honeycomb core based on the geometry of a single honeycomb cell and the material properties of the cell wall paper. The numerical model was benchmarked against CFRP/Nomex® Single Cantilever Beam (SCB) specimen tests and a closed-form semi-analytical model. The results show a close agreement between analytical, numerical and experimental energy release rate, as well as analytical and numerical mode-mixity. An extensive sensitivity analysis was also carried out and the effects of the geometry and the material properties of the SCB specimen on the energy release rate and mode-mixity have been investigated.

Adhesion strength of die attach film for thin electronic package at elevated temperature

Adhesion strength of a thin film for electronic packaging was investigated. The effects of temperature and loading rate on the adhesion were observed considering the viscoelasticity of adhesive. Various temperature conditions over the glass transition temperature of the adhesive were applied with controlled loading rates. A small hot plate was specially designed to control the temperature. Loading rate was controlled by a servo motor. A cantilever specimen was fabricated by two rectangular silicon chips. The adhesion was measured by a modified single cantilever beam method. Bending force was applied to the cantilever using rotatable jig. Adhesion strength was found to strongly depend on the temperature and loading rate. Below the glass transition temperature (Tg), the adhesion strength was increased with increasing loading rate. Near the Tg, the adhesion strength was decreased with increasing loading rate. Above the Tg, the adhesion strength did not significantly depend on the loading rate.