Showing papers in "Strain in 2006"

Digital Image Correlation: from Displacement Measurement to Identification of Elastic Properties – a Review

Abstract: The current development of digital image correlation, whose displacement uncertainty is well below the pixel value, enables one to better characterise the behaviour of materials and the response of structures to external loads. A general presentation of the extraction of displacement fields from the knowledge of pictures taken at different instants of an experiment is given. Different strategies can be followed to achieve a sub-pixel uncertainty. From these measurements, new identification procedures are devised making use of full-field measures. A priori or a posteriori routes can be followed. They are illustrated on the analysis of a Brazilian test.

A Comparative Study of Several Material Models for Prediction of Hyperelastic Properties: Application to Silicone-Rubber and Soft Tissues

Abstract: The correct modelling of constitutive laws is of critical importance for the analysis of mechanical behaviour of solids and structures. For example, the understanding of soft tissue mechanics, because of the nonlinear behaviour commonly displayed by the mechanical properties of such mate- rials, makes common place the use of hyperelastic constitutive models. Hyperelastic models however, depend on sets of variables that must be obtained experimentally. In this study the authors use a computational/experimental scheme, for the study of the nonlinear mechanical behaviour of biological soft tissues under uniaxial tension. The material constants for seven different hyperelastic material models are obtained via inverse methods. The use of Martins's model to fit experimental data is presented in this paper for the first time. The search for an optimal value for each set of material parameters is performed by a Levenberg-Marquardt algorithm. As a control measure, the process is fully applied to silicone-rubber samples subjected to uniaxial tension tests. The fitting accuracy of the experimental stress-strain relation to the theoretical one, for both soft tissues and silicone-rubber (typically nonlinear) is evaluated. This study intents also to select which material models (or model types), the authors will employ in future works, for the analysis of human soft biological tissues.

The Virtual Fields Method for Extracting Constitutive Parameters From Full‐Field Measurements: a Review

Abstract: The virtual fields method has been developed for extracting constitutive parameters from full-field measurements provided by optical non-contact techniques for instance. It is based on the principle of virtual work written with some particular virtual fields. This paper can be regarded as a general review summarising some 15 years of developments of this method. The main aspects of the method are first recalled in the case of both linear and non-linear constitutive equations. They are then illustrated by some recent relevant examples. Some studies underway as well as relevant issues to be addressed in the near future are eventually discussed.

Automatic Evaluation of Mixed‐mode Stress Intensity Factors Utilizing Digital Image Correlation

Abstract: A method for determining mixed-mode stress intensity factors from displacement fields obtained by digital image correlation is studied. To perform automatic evaluation, not only stress intensity factors but crack-tip location, higher-order terms in the series expansion of displacement fields and rigid-body displacement components are also determined simultaneously using nonlinear least squares based on the Newton–Raphson method. Experimental results show that the mixed-mode stress intensity factors are evaluated accurately from either radial or circumferential displacement components. As mixed-mode stress intensity factors can be evaluated easily, simply and automatically by the technique with digital image correlation and nonlinear least squares, it is expected that the proposed method can be applied to solve various fracture problems.

Characterisation of Contact Pressure Distribution in Bolted Joints

Abstract: The quantification of contact area and pressure distribution in a bolted joint is essential information, as it determines the integrity of the coupling. Current bolted joint design standards are based on analytical solutions of the pressure distribution, which, because of the inherent assumptions, frequently do not accurately represent the real conditions in a joint. This study uses a nonintrusive ultrasonic technique to quantify the contact pressure distribution in a bolted connection. The advantage of this experimental technique is that the effect of actual contact conditions can be determined. An ultrasonic wave is focused onto the clamped interface, and the reflected sound signal recorded. In areas where the contact pressure is high, most of the ultrasound is transmitted, and the reflected sound signal is weak. Whereas, when the contact pressure is low, the vast majority of the ultrasound is reflected back. A parallel experimental calibration is then used to find the relationship between the reflected sound signal and contact pressure. In this way, the pressure distribution in a clamped interface is determined for a series of different bolt torques. Two different interfaces were investigated: the first consisted of two ground surfaces clamped together, and the second a turned profile pressed against a ground surface. The effect of a washer underneath the bolt head was also considered. The turned profile was found to cause the contact to spread; there was also a certain degree of fragmentation leading to higher peak pressures than in the ground interface case. With a washer positioned under the bolt head for the turned case, the clamping performance of the bolt was improved. Good agreement was found when comparing the ultrasonic measurements with previous studies, with respect to the spread of the contact pressure distribution. However, in this study, the peak contact pressure was found to occur away from the edge of the bolt hole, and to be influenced by the edge of the bolt head.

Characterisation of Thermal Expansion Coefficient of Anisotropic Materials by Electronic Speckle Pattern Interferometry

Abstract: Carbon fibre composites find wide applications in aerospace, sporting goods industry and biomedicine. Mechanical and thermal properties of such materials are highly anisotropic; therefore, adequate experimental measuring methods are requested to determine them. This paper describes the application of electronic speckle pattern interferometry to full-field, real-time char- acterisation of the coefficient of thermal expansion (CTE) of anisotropic materials. The topics such as correlation fringes tilt and influence of small rigid body rotation were theoretically described and experimentally verified. A series of measurements was carried out to determine the CTE tensor for unidirectional and bi-directional carbon fibre laminates and to prove the feasibility of the method. The measuring set-up developed includes a temperature control unit for cooling and heating and a one-dimensional in-plane speckle interferometer.

Fracture and Ageing in Bone: Toughness and Structural Characterization

Abstract: The development of a mechanistic understanding of the increase in fracture risk in human bone with age is essential to public health. This represents a challenge for fracture mechanics as bone has a complex, hierarchical structure with characteristic features ranging from nanometer to macroscopic dimensions, and is thus much more complex than most engineering materials. In this study, we review ex vivo fracture experiments which quantitatively assess the effect of age on human cortical bone in the proximal-distal orientation, i.e. along the long axis of the bone. Specifically, cortical bone is seen to exhibit rising crack-growth resistance with crack extension; the toughness is consequently evaluated in terms of R-curves, measured in bones taken from a wide range of age groups (34-99 years). Both crack-initiation and crack-growth toughnesses were determined and were found to deteriorate with age; the initiation toughness decreases some 40% over the 65 years of ageing, while growth toughness is effectively eliminated over the same age range. The reduction in crack-growth toughness is considered to be associated primarily with a degradation in the degree of extrinsic toughening, in particular involving crack bridging in the wake of the crack. This explanation is supported by an examination of the micro-/nanostructural changes accompanying the process of ageing, performed using deep-UV Raman spectroscopy, computed X-ray tomography and optical/ electron microscopy.

Characterisation of Pressure‐sensitive Yielding in Polymers

Abstract: In this paper, the confined compression test set-up [Ma and Ravichandar (2000) Experimental Mechanics vol. 40, pp. 38–45] is employed to characterise the pressure-dependent yield behaviour of polymers. Attention is restricted to polymethyl methacrylate (PMMA) which is assumed to obey the Drucker–Prager yield function. The main objective is to develop a method for analysing the results of the above test procedure in order to obtain the pressure sensitivity index of the material. Furthermore, a technique for generating different stress histories in the specimen is explored by varying the initial clearance between the cylindrical specimen and the confining ring. In order to confirm the result obtained from the confined compression test, spherical indentation experiments in which high hydrostatic pressure is generated in the plastic zone underneath the indenter are carried out with the same PMMA material. The data obtained from these experiments are interpreted by performing finite element analyses assuming several values for the pressure sensitivity index of the material. It is shown that the hardness depends markedly on the above index. This dependence can be exploited to determine it from indentation experiments using an inverse approach.

Full-Field Displacement Measurement of a Speckle Grid by using a Mesh-Free Deformation Function

Abstract: In the present study, a combined experimental–numerical technique for the determination of the displacement and strain fields in the surface of a deformable body is described. The experimental part of this technique is based on the recording of the pair of images of the surface before and after deformation of the body, by means of a digital camera. This is done after spraying the surface with a random field of speckles (dots). Then the dots (having finite dimensions) of the second image are identified and uniquely paired with the dots of the first image. This permits the experimental determination of the deformation field in the surface. Then, by means of a mesh-free numerical method, a smoothed deformation field can be constructed. For that, the moving least square method is applied. The deformation field being available, the corresponding strain field can easily be obtained. Numerical simulation of this technique in three simple examples indicates that promising applications are expected.

Application of acoustic emission for masonry arch bridges

Abstract: There are over 40 000 masonry arch bridges in the UK, 60% of which are over 100 years old. The ever increasing levels of loading and volumes of traffic make it imperative that the condition, life expectancy and load capacity of such bridges are accurately assessed. Assessment procedures, however, generally rely on visual methods without giving any information on the internal condition of the structure. The acoustic emission (AE) technique has the ability to record certain types of damages anywhere within the structure before their effect becomes visible on the surface. Although AE is increasingly widely used for monitoring concrete and metallic bridges, its application for masonry bridges is currently very limited. A series of multi-ring brickwork arches have been tested as part of an extended study on fatigue performance of masonry arch bridges at the University of Salford. The present study attempts to assess the applicability of the AE technique for masonry arch bridges under static and long-term cyclic loading, to study crack propagation and failure mechanisms.

Relative Slip on Contact Surface under Partial Slip Fretting Fatigue Condition

Abstract: A combined experimental–numerical approach was utilized to characterize the relative slip along the contact surface and its features under the partial slip fretting fatigue condition. Relative displacements at two locations on the substrate (specimen) and fretting pad were measured in fretting fatigue tests. These measurements were then utilized to validate finite element analysis. Effects of the coefficient of friction on the relative slip and contact condition were investigated. The stress state along the contact surface was also investigated. Two contact geometries were analysed: cylinder-on-flat and flat-on-flat. There was no change in relative displacement between locations away from the contact surface because of the change in the coefficient of friction, while relative slip on the contact surface was affected by coefficient of friction. In addition, stick/slip sizes were affected by the change in coefficient of friction. Comparison between present and previous finite element models showed that stress state, as well as a critical plane-based crack-initiation parameter, was not much different between these approaches, while relative slip on the contact surface changed considerably.

Analysis of Nodular Cast Iron Microstructures for Micromechanical Model Development

Abstract: One of the main factors in determining the different grades of ductile iron is the matrix structure. In the as-cast condition, the matrix will consist of varying proportions of pearlite and ferrite, and as the amount of pearlite increases, the strength and hardness of the iron also increase. Three different nodular cast irons are here considered and their microstructure characterised in detail using metallographic methods. Then micromechanics models based on the unit cell approach and the finite element method are introduced to describe the actual constitutive response of the materials and the predicted behaviours are compared with experiments.

High Temperature Steam Pipelines – Development of the ARCMAC Creep Monitoring System

Abstract: Power stations are required to be designed and maintained to operate for long periods reliably and safely, ideally with the minimum need to close the plant down for servicing, inspection or other reasons. Typically the plant is licensed to operate for a period of 4 years until a major refurbishment and inspection outage is needed. However, essential is up-to-date recording of the remaining life of at least the highrisk areas of the plant. Monitoring these when the plant is in operation is not always possible or reliable and alternative methods are often required. One important need is to be able to assess the remaining life of components, particularly those identified as high risk. The network and orientation of the steam pipelines can make access for inspection and assessment purposes extremely difficult. The main steam pipes operate, for example, at pressures of 180 bar and temperatures of 568 C and require substantial lagging. The dimensions of the main steam pipes are typically of bore 240 mm and outside diameter 360 mm. The main threat to the integrity of the main steam pipe parent material is due to creep life exhaustion. Fortunately from design studies and operational experience of pipe degradation rates and failures, good information is available as to parts of the pipe system that need to be monitored to obtain reliable data on the remaining life of the pipes. Also known is that a good and feasible monitoring method to reveal the onset of failure processes is by the measurement of the increases in micro-strain generated in the outer skin of the pipe material, and this measurement can be made when the plant has been shut down during an outage. There are several methods to measure the change in micro-strain at designated points. Preferred, are more robust sensors that are little affected by the build up of scale on pipe surfaces and enable direct on-site physical measurements using optical methods. Pipe Life Assessment

Predicting Interfacial Loads between the Prosthetic Socket and the Residual Limb for Below-Knee Amputees-A Case Study

Abstract: In this study, an artificial neural network (ANN) was deployed as a tool to determine the internal loads between the residual limb and prosthetic socket for below-knee amputees. This was achieved by using simulated load data to validate the ANN and captured clinical load data to predict the internal loads at the residual limb–socket interface. Load/pressure was applied to 16 regions of the socket, using loading pads in conjunction with a load applicator, and surface strains were collected using 15 strain gauge rosettes. A super-position program was utilised to generate training and testing patterns from the original load/strain data collected. Using this data, a back-propagation ANN, developed at the University of the West of England, was trained. The input to the trained network was the surface strains and the output the internal loads/pressure. The system was validated and the mean square error (MSE) of the system was found to be 8.8% for 1000 training patterns and 8.9% for 50 testing patterns, which was deemed an acceptable error. Finally, the validated system was used to predict pressure-sensitive/-tolerant regions at the limb–socket interface with great success.

A Method of Combined SHPB Technique and BP Neural Network to Study Impact Response of Materials

Abstract: A new method combining the split Hopkinson pressure bar (SHPB) technique with the back-propagation (BP) neural network program is proposed. By this method, the treated strain wave signals become smooth with less noises induced by the transverse inertia. Moreover, the dynamic rate-dependent constitutive behaviour of materials can be identified, without any pre-assumption of a constitutive model. It is found that by taking the experimentally measured data of strain, strain rate and time as ‘input’ and the corresponding data of stress as ‘output’ of the BP neural network, the dynamic constitutive behaviour with internal damage or phase transformation evolution is easy to be identified, where the time could represent either the internal damage evolution or phase transformation process accompanied with the deformation process. It is emphasised that the data learnt by the BP neural network must include both loading and unloading processes, if the whole loading and unloading response is to be correctly predicted. The comparisons between the predictions and experimental results are in good agreement for both polyamide (PA) polymer (as an example of nonlinear viscoelastic materials) and Ti–Ni alloy (as an example of superelastic materials with stress-induced phase transformation).

Isochromatic Demodulation by Fringe Scanning

Abstract: RGB calibration is the fastest isochromatic demodulation technique, as it does not require unwrapping as in the case of phase-shifting method. The technique is based on constructing a look up table (LUT) of fringe order against RGB triplet from digital images and decoding the test image from the LUT. Research has shown that the technique, though very fast, is limited to fringe orders up to three with the conventional white light. The colours tend to merge beyond that and make it difficult to obtain a unique value of RGB triplet. Changes in fringe gradient caused by stretching/bunching of fringes in test model further add to errors. Special light sources with narrow- band spectral response are required with fringe tracking algorithms to demodulate higher fringe orders. The calibration technique is also sensitive to geometric and chromatic variations. This paper presents a cost-effective alternative solution to conventional RGB technique using a flatbed scanner. The system is capable of demodulating higher fringe order and incorporates information from other colour spaces. It does not require separate light sources and cameras, and is found to be insensitive to geometric and chromatic variations. Curve fitting technique has been proposed to determine accurate fringe orders.

Object grating method application in strain determination on ctod tests

Abstract: Standard fracture toughness tests require standard specimens with the presumption that mechanical properties are uniform in the crack growth direction. Standards for CTOD fracture tests prescribe remote crack mouth opening displacement-CMOD, which can lead to in-adequate results in the case of heterogeneous materials properties. This paper describes the application of an object grating method on the fracture behaviour of a heterogeneous specimen. Fracture behaviour is described by measuring deformation on the surface of a specimen, in terms of crack tip opening displacement and, consequently, by strain determination. An object grating method is advantageously used when measuring modified CTOD tests on two specimens with an initial crack in a macroscopic heterogeneous welded joint. Results significantly show that fracture behaviour depends on the material in the vicinity of the crack tip concerning the direction of crack propagation.

Deformation Analysis of Notched Rubber Specimens

Abstract: The influence of the initial crack tip radius on the strain distribution in the vicinity of the blunted crack tip was determined experimentally by an optical full-field strain analysis method. These experimental results were compared with the calculations of the commercial finite element code ABAQUS 6.4-1. For the simulation a suitable hyperelastic material law was chosen and fitted to experimental data of three different tests (uniaxial tensile, planar tensile, biaxial tensile). Two different elastomer grades (SBR and EPDM) were selected for the experimental work. The utilized optical full-field strain analysis method based on the image correlation technique was found to be an effective tool to determine strains, strain distributions and gradients near to the crack tip for elastomeric materials. Different material behaviour was observed for the two rubber types investigated. While the crack tip was regularly blunted (half circle shape) for EPDM and the strain gradient was low (less steep), the crack tip was sharp (less blunted) with a higher strain gradient for SBR.

A Probabilistic Evaluation of the Least Squares Strain Tensor Derived from a Three‐Dimensional Modular Strain Rosette Using the Monte‐Carlo Technique

Abstract: Strain gradients give rise to a number of problems in the field of embedded three-dimensional strain measurement. In order to avoid these problems a modular type three-dimensional strain rosette was embedded into known strain fields and the data from the individual gauges compared with theoretical predictions. Finally, the least squares strain tensor was predicted from experimental data analysed using the Monte-Carlo technique and the theoretical results forecast from finite element data taking into account the mechanical properties of the carrier, plug and prismatic bar. Some of the experimental results were found to correlate well with the theoretical values but some values in the least squares strain tensor, in particular under compression and torsional loading, departed considerably from the theoretical values. It was found that the effect of the measurement errors in the individual gauges combined with the matrix operations in the least squares strain tensor were responsible for biasing the resultant tensor data. However, the modular technique provided a solution to the problem of strain gradients.

An Interlaminar Strain Measurement for Insulation Panels of LNG Carriers

Abstract: The aim of the study was to investigate the dynamic failure initiation as well as the failure modes of insulation panels of liquefied natural gas (LNG) carriers. Insulation panels of LNG cargo tanks may include mechanical failures such as cracks as well as delaminations within the layers because of impact sloshing loads and fatigue loadings, and these failures cause a significant decrease of the structural safety. In this study, a structural health monitoring system was developed that employs fibre optic sensors for monitoring various failures that can occur in LNG insulation panels. Fibre optic sensors have the advantage of being embedded inside the insulation panels. The measurement signal of embedded fibre optic sensor is used to calculate the strain distribution within insulation panels and is analysed to identify the damage initiation. It has been observed that the presence of defects and delaminations produce noticeable changes in the strain measurement in a predictable manner. In addition, fibre optic sensors are used to measure static and dynamic strain variations with and without damage. It is expected that this study will be used as a fundamental study for the safety assessment of LNG insulation panels.

Applicability of Optical Geometric Differentiation for Time‐average Geometric Moiré

Abstract: Optical experimental method for analysis of derivatives of dynamic displacements from patterns of time-average moire fringes is proposed in this paper. Derived analytical relationships for one-dimensional optical model are validated for two-dimensional elastic structures performing in-plane vibrations. The fact that digital image filtering techniques are normally required for the identification of time-averaged super-fringes does not lessen the practical value of the proposed method.

Range of Applicability of the Method of Caustics around Holes

Abstract: The range of applicability of the optical method of caustics, which is based on plane stress conditions, around cylindrical holes in plane specimens is investigated. The position of the generatrix curve of the caustic and the conditions, which influence its size, are defined. The dimensions of the specimen, the ratio of the thickness to the diameter of the hole, the applied stress and the dimensions of the optical set-up influence the position of the generatrix curve of the caustic. At a critical distance from the boundary of the hole the state of stress degenerates from three-dimensional to plane stress. In this paper, the extent of this region was defined by finite element analysis, in case of uniaxial tension. The defined critical distance was correlated with the condition, which influence the caustic, thus the range of applicability of the method of caustic around hole was defined. The validity of this range was experimentally checked.

Investigation of Analytical Solutions for Bonded Structures by Photomechanical Methods

Abstract: In this paper, both photoelasticity and moire interferometry were successively incorporated with finite element method to investigate the predicted thermal stresses and lateral displacement of bonded structures calculated from different theories. It was found that the distributions of moment and transverse force play significant roles in making different values of thermal stresses in the adherends by authors’ and Suhir's 1986 theories. On the other hand, the values of lateral displacement obtained from different theories are almost identical.

A Measurement Method for Birefringent Plate using Elliptically Polarized Light

Abstract: The principal axis ψ and total relative phase retardation ρtot of a birefringent plate are obtained automatically using an elliptically polarized incident light source and a phase unwrapping technique The technique overcomes the error associated with the quarter-wave plate by making use of incident light of different wavelengths, and the unwrapping technique allows ψ and ρtot to be determined using an arctangent function without interpolation or construction of a calibration table The proposed method is validated analytically and experimentally for a circular disk under diametral compressive load

The Post‐Yield Behaviour of an Internally Pressurised Cylinder having a Pad Attachment

Abstract: A study of pressurised cylinders having attached pads was made. The possibility of a fatigue crack developing along one side of the pad was noted. For both defect-free components and components having axial crack-like defects, finite element and limited experimental studies of the local and global deformations were made and results were found to be in close agreement. Both welded and integrally machined pads were studied. It was observed that for defect-free components, the method of pad attachment has little effect on the burst pressure. The presence of a pad was found to increase the burst pressure of cracked components by a small but significant margin. A finite element-based parametric study of pipes with part-penetrating defects and a range of pad geometries has demonstrated that pad size has little influence on the limit load for any of the cracked cases considered. However, pipes with penetrating defects were strengthened by the presence of pads, particularly for thin-walled sections.