Non-uniform Shrinkage Research Articles

Comprehensive numerical modelling of the hot isostatic pressing of Ti-6Al-4V powder: From filling to consolidation

Hot Isostatic Pressing (HIP) is a manufacturing process for production of near-net-shape components, where models based on Finite Element Method (FEM) are generally used for reducing the expensive experimental trials for canister design. Researches up to date implement in the simulation a uniform powder relative density distribution prior HIPping. However, it has been experimentally observed that the powder distribution is inhomogeneous after filling, leading to a non-uniform tool shrinkage. In this study a comprehensive numerical model for HIPping of Ti-6Al-4V powder is developed to improve model prediction by simulating powder filling and pre-consolidation by means of a two-dimensional Discrete Element Method (DEM). Particles’ dimension has been scaled up in order to reduce the computational cost of the analysis. An analytical model has been developed to calculate the relative density distribution from powder particle distribution provided by DEM, which is then passed in information to a three-dimensional FEM implementing the Abouaf and co-workers model for simulating powder densification during HIPping. Results obtained implementing the initial relative density distribution calculated from DEM are compared with those obtained considering a uniform relative density distribution over the powder domain (classic approach) at the beginning of the analysis. Experimental work has been carried out for validating the DEM (filling) and FEM (HIP) model. Comparison between experimental and numerical results shows the ability of the DEM model to represent the powder flow during filling and pre-consolidation, providing also a reliable values of the relative density distribution. It also highlights that taking into account the non-uniform powder distribution inside the canister prior HIP is vital to improve numerical results and produce near-net-shape components.

Influence of specimen geometries and drying conditions on concrete cracking in restrained elliptical ring tests

Abstract The restrained shrinkage elliptical ring test has been established as an efficient method for assessing the cracking potential of concrete at early ages because an elliptical ring can provide a higher degree of restraint compared with a circular one. In this study, a series of circular and elliptical concrete rings restrained by steel rings with various thicknesses were tested under top & bottom surfaces drying or outer circumferential surface drying. By comparing concrete cracking age under different geometrical and drying conditions, the effects of ring geometry, restraining steel ring thickness and drying condition on the cracking process in concrete rings were revealed. Furthermore, numerical analyses were conducted to investigate the fracture mechanism for circular and elliptical rings by applying a fictitious temperature field to simulate the shrinkage effect of concrete. It is found that the increase of steel ring thickness can enhance the degree of restraint, therefore shorten the cracking age for both circular and elliptical rings. However, the improvement is more significant for circular rings. The fracture processes under the two drying conditions, i.e. top & bottom surfaces drying and outer circumferential surface drying are completely different: for drying from outer circumferential surface, the crack initiates at the outer surface and propagates towards the inner surface; for drying from top & bottom surfaces, the crack initiates partially along the height direction at the inner circumference of a concrete ring, and propagates along the radial direction, step by step, until the crack propagates throughout the whole ring wall. In both cases, the self-restraint caused by the non-uniform shrinkage of concrete and the external restraint from the inner steel ring contribute the driving effects for crack propagation. In general, compared with circular rings, the elliptical rings demonstrate the advantage of providing a higher degree of restraint. The elliptical ring test method can, therefore, supplement the traditional circular ring test method for assessing cracking tendency of concrete with higher cracking resistance.

Effects of moisture gradient of concrete on fracture process in restrained concrete rings: Experimental and numerical

The non-uniform shrinkage caused by moisture gradient in concrete provides self-restraint, which has a significant effect on the assessment of cracking potential of concrete through the restrained shrinkage ring test. Furthermore, moisture gradient in concrete would be also affected by concrete strength because concretes designed for different strength grades usually have different water to cement ratio. In this paper, three series of circular and elliptical concrete rings with a 37.5 mm thick wall and three distinguished concrete strength grades of C30, C50 and C80 were tested to investigate the effect of the moisture gradient on crack initiation and propagation in restrained concrete rings. An integrative model based on the nonlinear diffusion theory is introduced to calculate the moisture distributions in concrete rings, and the fictitious temperature fields are derived for the simulation of the shrinkage effect in concrete. Meanwhile, a fracture mechanics-based numerical method is proposed to analyze the crack initiation and propagation in a concrete ring in the restrained ring test. The effects of ring geometry, concrete strength and uniform/non-uniform shrinkage assumption on the cracking initiation and propagation process are elaborated. The results indicate that the non-uniform shrinkage in concrete provides driving energy for concrete cracking, which is approximately 40% of the total driving energy. Accordingly, it significantly affects the crack initiation position and propagation direction, occurring at the outer surface and propagating toward the inner surface of the concrete ring. With the increase of concrete strength, the cracking potential of restrained concrete ring increases and the proportion of the self-restraint caused by the non-uniform shrinkage in the total restraint decreases because of the reduced moisture distribution.

Influence of manufacturing process on the strength of composite materials

Residual stresses in laminated composites induced by non-uniform matrix solidification and shrinkage through manufacturing process may lead to the shape distortion and possible damage of the final product. In this work, the phase transition model for matrix material was numerically implemented into Abaqus software to simulate evolution of stiffness properties and development of residual stresses of composite laminate during manufacturing temperature cycle. This simulation shows the presence of significant residual stresses in composites even before mechanical processing of the material. As an example, the residual stresses were computed for the plate with cross-ply layup. As a last step two specimens with presence of residual stresses and without one were loaded up to failure using progressive damage model. Modelling results show essential influence of residual stresses on distribution and development of matrix cracks, failure modes and strength values.

Predicting shrinkage induced curvature in plain and reinforced concrete

Shrinkage induced curvatures in reinforced concrete elements are thought to be affected only by section geometry and distribution/ratio of reinforcement. The variation in the level of internal restraint caused by the non-uniform distribution of concrete constituents within the section, however, can also lead to additional shrinkage induced deformations, and potentially to larger than expected deformations in critical structural elements, even under service conditions. This study examines experimentally the development of non-uniform shrinkage strains in unreinforced as well as symmetrically and asymmetrically reinforced concrete elements. Results confirm that shrinkage is non-uniform due to the variations in internal restrains (coarse aggregates and reinforcement). The addition of steel fibres mitigates this effect and reduces overall shrinkage curvature. A prediction model for shrinkage induced curvature of plain and reinforced concrete is proposed, taking into account the non-uniform distribution of concrete constituents. The proposed model yields results in good agreement with experimentally observed values of shrinkage curvature and can be used to improve the predictions of design guidelines.

Shrinkage and flexural behaviour of free and restrained hybrid steel fibre reinforced concrete

The effect of restrained shrinkage on the mechanical performance of concrete and steel fibre reinforced concrete (SFRC) requires more investigation, especially when using recycled tyre steel fibre (RTSF). This paper examines the free and restrained shrinkage strains and the mechanical performance of seven SFRC mixes. Results show that both free and restrained average shrinkage strains are very similar in all blends of fibres and they exhibited non-uniform shrinkage through the height of the section. All examined blends meet strength requirements by MC-2010 for fibres to replace part of the conventional reinforcement in RC structures.

The influence of heat on shrinkage and water absorption of Dendrocalamus giganteus bamboo as a functionally graded material

The main objective is to present the results of an investigation on the effect of heat and time exposure on hygroscopic property of Dendrocalamus giganteus bamboo. The shrinkage and water absorption of bamboo segments in longitudinal, radial and tangential directions, due to heat effect of seven different temperatures from ambient to 225 °C during 3 h and 24 h has been investigated. An equation based on the principal of curve fitting has been established for rapid, transition and slow phases of water absorption. The non-uniform shrinkage and water absorption tests in tangential direction at different temperatures during 3 h carried out to obtain the fiber and matrix shrinkage and water absorption separately. The water absorption test result shows that by increasing the temperature and time exposure the hygroscopic property of bamboo is reduced. Subjecting to heat at higher temperatures can slow down the rate of water absorption in short term.

Analysis of Non-Uniform Shrinkage Effect in Box Girder Sections for Long-Span Continuous Rigid Frame Bridge

To consider the effect of non-uniform shrinkage of box girder sections on the long-term deformations of continuous rigid frame bridges, and to improve the prediction accuracy of analysis in the design phase, this paper proposes a new simulation technique for use with general-purpose finite element program. The non-uniform shrinkage effect of the box girder is transformed to an equivalent temperature gradient and then applied as external load onto the beam elements in the finite element analysis. Comparative analysis of the difference in deflections between uniform shrinkage and nonuniform shrinkage of the main girder was made for a vehicular bridge in reality using the proposed technique. The results indicate that the maximum deflection of box girder under the action of non-uniform shrinkage is much greater than that under the action of uniform shrinkage. The maximum downward deflection of the bridge girder caused by uniform shrinkage is 5.6 mm at 20 years after completion of bridge deck construction, whereas the maximum downward deflection caused by non-uniform shrinkage is 21.6 mm, which is 3.8 times larger. This study shows that the non-uniform shrinkage effect of the girder sections has a significant impact on the long-term deflection of continuous rigid frame bridge, and it can be accurately simulated by the proposed transformation technique.

Investigation of non-uniform gelation effects on residual stresses of thick laminates based on tailed FBG sensor

Due to the appearance of temperature gradient and non-uniform gelation, fully understanding of residual stresses is even more complex in thick laminates. In this paper, basic mechanisms of cure process were presented firstly. Then, experimental investigation of the non-uniform gelation was carried out together with characterization of necessary material properties. Tailed FBG sets were applied to monitor the cure of thick laminates with temperature gradient. The non-uniform gelation and chemical shrinkage gradient were captured successfully. Lastly, FEM analysis integrating thermal-chemical sub-model and stress-displacement sub-model was carried out to reveal the development of residual stresses. It is demonstrated that the high temperature layer gelled earlier and showed more chemical shrinkage. The chemical strain gradient would introduce compression internal stresses in prior gelled layer and introduces tensile internal stresses in later gelled layer. For the case studied here, transverse residual stress generated by non-uniform chemical shrinkage is small. The strategy used here is promising to estimate the residual stresses for more complex cases further.

THE INFLUENCE OF OWN STRESSES ON TENSILE CONCRETE STRENGTH

Based on experiments results brittle duralumin samples, effect on stresses concrete (mortar) strength caused by non-uniform cross-section shrinkage (when dried) or expanding (when moistened) was inevitable. Various authors’ experiments results diversity on concrete (mortar) tensile strength of moistening and drying effect were analyzed. Reasons for increasing air-dry concrete (mortar) strength storage at beginning of humidification were explained. Wetting sample duration (intensity) effect on concrete strength was analyzed in detail and opposite results causes on concrete strength moistening (drying) effects were obtained and justified.

Service design approach for composite steel–concrete floors

Composite steel–concrete floors are widely used throughout the world for building and bridge applications. One of their main advantages relies on using the steel sheeting as permanent formwork and, once the concrete has hardened, as external reinforcement. This form of construction finds applicability in both steel and concrete structures with the use of composite slabs and post-tensioned composite slabs, respectively. For building applications, the design of composite steel–concrete floors is usually governed by serviceability limit state requirements associated with deflections. This paper presents a new design approach for the service design of composite and post-tensioned composite slabs. The particularity of the proposed procedure relies on the ability to account for the non-uniform shrinkage profile which develops through the slab thickness when the concrete is cast on steel sheeting. This behaviour is caused by the presence of the sheeting, which prevents drying from occurring from the underside of the slab. The proposed approach is validated against experimental measurements available in the literature for full-scale long-term tests of composite slabs and post-tensioned composite slabs.

Identification of the hygro-thermo-chemical-mechanical model parameters of concrete through inverse analysis

A wide range of parameters is required in input when applying hygro-thermo-chemical-mechanical models to concrete components with the aim of determining the variations over time of temperature, relative humidity and shrinkage induced deformations. While a sub-set of these material parameters can be evaluated on the basis of the concrete mix specifications or from literature data, this paper presents a robust inverse analysis procedure for the identification of the remaining sub-set of parameters that are characterised by a large variability and, in some cases, do not have a precise physical meaning and are not amenable to a direct measurement. The particularity of this paper is to propose different strategies for the characterisation of these material parameters that account for the presence of different exposure conditions, as these affect the outcomes and requirements of the parameter identification procedure. After introducing the adopted hygro-thermo-chemical-mechanical model, representative results of an extensive sensitivity analysis are presented in the first part of the paper to give insight into most effective number, location and duration of measurements to be used in input of the inverse analysis. The inverse analysis procedure is then presented and applied to a number of selected scenarios to highlight its robustness considering different boundary conditions in terms of external temperature and relative humidity surrounding the concrete. The ability to characterise these parameters will support a wider use of these hygro-thermo-chemical-mechanical models, especially for those applications in which humidity and temperature profiles significantly influence the structural response, for example when predicting curling in industrial pavements and non-uniform shrinkage profiles in composite steel-concrete slabs.

Symulacje deformacji wyprasek z uwzględnieniem utwierdzenia wynikającego z montażu

The paper deals with the influence of part assembly on deformation of plastic part produced with injection molding technology. Parts tend to deform because of non-uniform shrinkage, which can be predicted with CAE injection molding software. Calculations usually do not consider the application of the part. In this paper, several examples were used to present the influence of assembly on the shape of the part.

More comprehensive 3D modeling of clay‐like material drying

Drying process plays an important role in the manufacturing of many products such as ceramic, kitchenware and building materials, some of which have complex three‐dimensional (3D) geometry. To deal with many restrictions found in literatures, a 3D numerical approach was used to describe the drying process of a porous Clay‐like material. The problem investigated involves highly coupled equations considering heat, mass, and mechanical aspects. The model is validated through the comparison of experimental measurements with simulation result. Simulation results show that increasing the initial moisture content and reducing the initial temperature have the same privilege and without significant increase in drying time, it reduces slightly the amount of maximum stress but delays the occurrence time of maximum stress. The nonuniform heat expansion induced stresses are very small in comparison to nonuniform moisture shrinkage induced stresses and can be neglected in drying simulation. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1469–1478, 2018

Application of 3D-DIC to characterize the effect of aggregate size and volume on non-uniform shrinkage strain distribution in concrete

To elucidate the effect of aggregate size and volume on the non-uniform strain distribution in concrete, drying shrinkage of mortar and concretes were determined with 3D digital image correlation (3D-DIC). The distribution of shrinkage displacements and strains in mortar and concrete were analyzed. The results show that 3D-DIC makes it possible to measure non-uniform displacement distributions initiated by shrinkage in mortar and concrete. The non-uniformity became more remarkable with drying time. The presence of aggregates larger than 5 mm in concrete have locally changed the displacement and strain fields. Aggregates within 5–25 mm make non-uniform strain of concrete more fluctuant, especially when the aggregate size is larger than 10 mm. The maximum and minimum principal strain distributions became more heterogeneous with decreasing volume of aggregates.

Permeability evolution and mesoscopic cracking behaviors of liquid nitrogen cryogenic freeze fracturing in low permeable and heterogeneous coal

Fracking to approach permeability enhancement is indispensable to enhance coalbed methane recovery, which can significantly reduce greenhouse gas emissions and produce substantial clean energy. To access efficient fracking, samples of Permian low permeable coal reservoir were cracked into different sizes or scales of blocks and particles with liquid nitrogen cryogenic freeze fracturing (FF) by maximizing the underlying heterogeneity of coal. To investigate the crack efficacy, this study systematically examined the permeability evolution and mesoscopic cracking behaviors of coal with different water contents and cleat–fracture systems in the context of cryogenic FF. Results showed that the permeability enhancement and microcracking tended to occur with increasing water content of coal sample; and the efficacy of cryogenic FF on the tighter coal sample was more remarkable. However, the permeability does not strictly increase with the cycles of cryogenic FF and has a close relationship with water content, structural plane direction, efficacy of cryogenic FF, and porosity compaction. The mesoscopic cracking behaviors indicate that numerous smaller pores are iteratively, not strictly sequentially, cracked and become connective in this process. The permeability evolution of coal sample is identified as significantly associated with the mesoscopic cracking behaviors. Notably, the first cycle of cryogenic FF acted on the detected several scales of pores and micro fissures, and partially caused these structures to be opened and interconnected to be permeable. Two main changes were observed in the microcracking of the coal samples in this study: 1) nonuniform shrinkage deformation and micro fissure expansion; and 2) pores opening mostly in the macropore and mesopore scale. It is reasoned that thermal cracking and intermittent opening of seepage pores due to the phase transition of free water in pores or micro fissures ultimately contribute to the permeability enhancement in low permeable and heterogeneous coal.

The fracture mechanism of circular/elliptical concrete rings under restrained shrinkage and drying from top and bottom surfaces

Due to uniform shrinkage along the radial direction, drying from both top and bottom surfaces has been recommended to replace drying from outer circumference surface in the restrained circular ring test to assess cracking tendency of concrete. However, non-uniform shrinkage along the height direction under drying conditions is significant, and its effect on crack initiation and propagation in a concrete ring is not clearly understood. To investigate the fracture mechanism of the restrained ring test under drying from top and bottom surfaces, three series of circular and elliptical ring specimens with heights of 30 mm, 50 mm and 75 mm are tested to measure the cracking ages. A fracture mechanics based numerical method is proposed by introducing fictitious crack model to simulate the fracture process and predict the cracking age of a concrete ring under restraint. The effects of ring geometric profile, specimen height and moisture gradient on crack development are discussed. The results indicate that, under drying from both top and bottom surfaces, crack initiates partly along the height direction at the inner circumference of a concrete ring, and propagates along the radial direction, one by one, until the crack propagated throughout the whole cross-section. The moisture gradient along the height direction has significant effect on the crack driving force, which is dominated by the moisture gradient and steel ring restraint near the exposed surface, whose proportion increases with the increase in distance from the exposed surface.

Effect of section geometry on development of shrinkage-induced deformations in box girder bridges

Non-uniform shrinkage strains can lead to significant additional deflections in large box girder bridges, leading to serviceability problems. This article examines experimentally and analytically the effect of different cross-section geometries on the shrinkage camber of bridge box girders. Small-scale beams were tested to determine the development of shrinkage strains across the beams of depth. Parameters investigated include cross section thickness, drying conditions, and type of concrete mix. Based on the experimental results, inverse analysis is utilised to obtain a surface factor and a hydro-shrinkage coefficient. In this study, such vales are used to determine, for the first time, shrinkage-induced bending deformations of long-span bridges using a hydro-mechanical approach. The results are then used to examine numerically the effect of different section geometries on the development of shrinkage camber. It is shown that the analytical predictions match the experimental results with an accuracy of 85%. A further parametric study is carried out to investigate the effects of specimen geometry and ambient relative humidity. The hydro-mechanical approach is further validated using shrinkage field data from the 230 m two-span box girder Yiju River Bridge (China). The approach proposed in this study is expected to contribute towards improving the predictions of the long term behaviour of box girder bridges and towards better bridge management.

Tissue shrinkage in microwave thermal ablation: comparison of three commercial devices

Purpose: To evaluate, characterise and compare the extent of tissue shrinkage induced from three different commercial microwave ablation devices, and to elucidate the mechanism behind the distinctive performances obtained.Materials and methods: Microwave ablation (N = 152) was conducted with three different commercial devices on cubes of ex vivo liver (10–40 ± 2 mm/side) embedded in agar phantoms. 50–60 W was applied for 1–10 min duration. Pre- and post-ablation dimensions of the samples, as well as the extent of carbonisation and coagulation were measured and correlated. ANOVA was performed to evaluate statistical significance.Results: For all devices, logarithmic correlations with time were observed for both tissue shrinkage (R2 = 0.84–1.00) and induced carbonisation (R2 = 0.73–0.99) radially to the antenna axis. Along the longitudinal axis of the antenna, for two of the devices shrinkage did not appreciably change with time (p > 0.05), yet carbonisation increased linearly (R2 = 0.57–0.94). For the third fully internally-cooled device, both carbonisation and shrinkage showed logarithmic trends (R2 = 0.85–0.98 and R2 = 0.78–0.94, respectively) based upon delayed carbonisation appearing only 5 min into ablation and onward. For all devices, non-uniform shrinkage was noted within the coagulated area increasing from the boundary of the ablated area (14%) to the limit of carbonisation (39%) in a linear fashion (R2 = 0.88)Conclusions: Microwave ablation device construction can alter the extent of post-ablation coagulation and tissue shrinkage. Given that tissue shrinkage in the coagulated area shows non-uniform behaviour, observed differences can be attributed in part to the applicator cooling system that alters the ablation temperature profile.

Erratum to: Non-uniform shrinkage of multiple-walled carbon nanotubes under in situ electron beam irradiation

The online version of the original article can be found under doi: 10.1007/s00339-016-0418-8 .