Initial Strain Energy Research Articles

Strength and Crack Propagation Analysis of Layered Backfill Based on Energy Theory

The strength of backfill is greatly influenced by its inclination angle and interlayer concentration. In order to study the influence of inclination angle and interlayer mass concentration on the strength of backfill, a group of layered cemented backfill with cement-sand ratio of 1:4, interlayer mass concentration of 66%, 67% and 68% and inclination angles of 0°, 10°, 20° and 30° were prepared by using tailings as aggregate. The uniaxial compression test was carried out to analyse the effect of interlayer mass concentration and inclination angle on layered cemented backfill. The crack propagation and energy change law of the specimen during compression were analysed by J-integral and energy conservation law. The relationship between the crack initiation and propagation and strain energy of two representative three-layer backfill specimens was analysed by numerical modelling. The results show that the increase in the layer number and the inclination angle of the backfill can weaken the strength of the backfill. In a certain range of inclination angles, the weakening coefficient of the backfill caused by the inclination angle is very consistent with the cosine value of the corresponding angle. Due to the release of crack energy and the existence of interface J integral, the uniaxial compressive strength of different mass concentration backfill is different at various positions. When the displacement reaches a certain value, the crack and strain energy no longer increase.

Deep learning-based 3D multigrid topology optimization of manufacturable designs

Structural topology optimization is a compute-intensive process due to several iterations of simulations required to evaluate the performance of the component during optimization. Deep learning (DL) based approaches can address this challenge, but these methods were demonstrated mainly using 2D shapes and, at best, in low-resolution 3D geometries (typically 323). Further, due to non-manufacturable geometric features, the predicted optimal geometries from DL may not be manufacturable, even using additive manufacturing. In this paper, we develop a DL framework using a multigrid convolutional neural network (CNN) to generate high-resolution topology-optimized 3D geometries with additional checks on the manufacturability of the predicted shapes. Our framework predicts the final optimal topology using the initial strain energy (objective function of structural topology optimization) and target volume fraction (material fraction to be preserved after optimization) as input. We train the network using a multigrid approach, which enables topology optimization at 1283 resolution, which was previously computationally challenging. We first train the multigrid CNN at a lower resolution and then transfer the learned network to continue training at higher resolutions. We use a distributed deep learning framework on a GPU supercomputing cluster to further speed up the training time. Distributed DL significantly speeds up the training time by more than 4× while achieving similar model performance. Finally, we check the optimal geometries for manufacturability using fused deposition modeling (FDM)-specific manufacturability constraints. The large training dataset (>60,000 high-resolution topology optimization examples) will be released with the paper to enable further research on this topic.

Mode-II progressive fracture of sawn timber and timber-adhesive bond: experimental evaluation of end notched flexure (ENF) testing using DIC

The end-notched flexure (ENF) testing technique has been used in this paper to investigate the Mode II fracture behaviour of sawn timber and timber-adhesive bonds. Mode-II strain energy release rates were obtained by using classical data reduction schemes based on actual crack lengths captured using digital image correlation (DIC) technique. The compliance-based beam method (CBBM), which does not require the actual crack length measurements, was also evaluated for its suitability for Mode-II fracture of timber. Utilizing forward shear slip measurement from DIC at every millimetre of crack length, a simple yet effective and innovative technique to identify crack tip opening and to monitor crack length has been proposed herein. Three different initial notch widths were used in the current study to examine their suitability in producing reliable crack initiation and consistent bond delamination in solid timber and glued timber. The strain energy release rates calculated from the actual crack and equivalent crack length values showed similar trends in fracture resistance curves, which are commonly known as R curves, but the initial strain energy release rate (GII0) and the critical strain energy rate (GIIC) obtained from the two methods showed some discrepancies. Equivalent crack method CBBM was found to be inadequate in determining a consistent initial strain energy release rate despite producing a stable and steady fracture energy after crack initiation. Experimental results showed that Mode-II timber-adhesive bond line fracture is relatively more brittle than timber fracture, and the average critical strain energy release rate of timber-adhesive bond (GIIc) was 14% greater than that of sawn timber. Based on experimental observations, specific test criteria for ENF testing of timber structures are proposed in this paper.

Study on the synergistic effect of carbon nanofillers on the interlaminar toughness of fibre metal laminates

Delamination failure is the main damage mode of fibre metal laminates (FMLs), including the combination of aluminium alloy and glass fibre reinforced epoxy. The present study focuses on the mode I interlaminar fracture toughness of FMLs with dispersion and synergy in resin matrix of two different carbon nanofillers, layered Graphenes (GNPs) and Multi-Walled Carbon Nanotubes (MWCNTs). The double cantilever beam (DCB) was implemented to test the mode I strain energy release rate (GΙC) of FMLs with a fixed content (1 wt%) of GNPs, MWCNTs and GNPs/MWCNTs at 1:1. The addition of carbon nanofillers has positive effect on the interlaminar performance of FMLs. The initial strain energy release rate (GΙC,ini) values of FMLs with GNPs and MWCNTs are 0.369 and 0.475 KJ/m2, which represent increases of 8.87 % and 40.1 %, respectively. The maximum GΙC,ini value of GNPs/MWCNTs modified FMLs is 0.672 KJ/m2, which represents a 98.2 % increase. Scanning Electron Microscopy (SEM) reveals the mechanism of hybrid toughening. During the mode I crack propagation process, the synergistic effect of the two nanofillers is more useful in the interlaminar fracture toughness.

Cyclic fracture simulation through element deletion in structural steel systems

This paper presents a finite element-based model for direct simulation of cyclic fracture in steel components and connections with application to predicting failure and collapse of steel structures. The formulation couples a plasticity model for large deformations that captures plastic work stagnation and the Bauschinger effect with a two-stage damage model to simulate fracture initiation, propagation, and failure through an element deletion strategy. The model includes the non-proportional loading and load-history effects in the fracture initiation and propagation process. Fracture initiation and propagation is controlled using new fracture initiation strain and fracture energy surfaces with stress triaxiality and Lode angle dependance that can represent different fracture behaviors. Model calibration is discussed for common grades of structural steel, weldments and bolts using typical material tests. The model capabilities are validated against experiments including ancillary material tests, components, and subassemblies of steel structures that experienced fracture subjected to monotonic and cyclic loading. A culminating validation is conducted on a four-story steel frame structure tested to collapse. The proposed model provides a robust and valuable tool for stability analysis and simulations of damage and collapse triggered by fracture in components and connections of three-dimensional steel structures subjected to extreme loads.

Design of an innovative laser-assisted four-point bending forming process for high-stiffened structure of aluminum alloy

High-stiffened structures of aluminum alloy are commonly used on modern aircrafts to meet the requirements of light weight and high stiffness. In this study, the combination of the laser scanning and four-point bending called laser-assisted four-point bending (LAFPB) was proposed to form the high-stiffened structures of aluminum alloy to the product quality. With the analytical model, simulation and experimental bending results, the forming characteristics of LAFPB were investigated. The main results show that the increase of the plastic strain was originated from the elastic strain of the laser scanned area and the “bullying effect” of the adjacent areas which brought about by the mechanical balance reconstruction. In the laser-assisted four-point bending, the initial elastic strain energy inside the part is converted into plastic strain energy under the action of the laser, the plastic strain energy of the workpiece increased by about 250%. It is proved by simulation and experiment that LAFPB can reduce the mechanical force and springback at the same deformation compared with traditional press bending which make a foundation for improving forming quality of high-stiffened structure parts.

Machining Distortion Minimization of Monolithic Aircraft Parts Based on the Energy Principle

Machining distortion is a recurring problem in the machining of monolithic aircraft parts. This paper aims to study the machining distortion minimization of monolithic aircraft parts. Firstly, the energy principle of machining distortion was analyzed. Then, a rapid prediction model of the final part distortion for beam parts was proposed based on the equivalent stress, and the initial bending strain energy contained in the final part was used to characterize the bending distortion risk of the final part. Numerical simulation and milling experiments verified the effectiveness of the proposed prediction model. The relative error between the experimental and calculated results does not exceed 26.5%. Finally, the influence of initial residual stress fluctuation, part geometry and the part location on part distortion was analyzed from the energy point of view. The obtained results indicated that the expected final part distortion can be minimized by adjusting these three factors.

Energy principle and material removal sequence optimization method in machining of aircraft monolithic parts

In the machining process of aircraft monolithic parts, the initial residual stress redistribution and structural stiffness evolution often lead to unexpected distortions. On the other hand, the stress redistribution and stiffness reduction during the machining process depend on the material removal sequence. The essence of the stress redistribution is releasing the initial elastic strain energy. In the present study, the influence of the material removal sequence on the energy release is studied. Moreover, a novel optimization method is proposed for the material removal sequence. In order to evaluate the performance of the proposed method, the mechanism of the machining distortion is firstly analyzed based on the energy principle. Then a calculative model for the machining distortion of long beam parts is established accordingly. Moreover, an energy parameter related to the bending distortion and the procedure of the material removal sequence optimization is defined. Finally, the bending distortion analysis and material removal sequence optimization are performed on a long beam with a Z-shaped cross-section. Furthermore, simulation and experiments are carried out. The obtained results indicate that the optimized sequence results in a low distortion fluctuation and decreases the bending distortion.

Relationship between strain energy and fracture pattern morphology of thermally tempered glass for the prediction of the 2D macro-scale fragmentation of glass

This work deals with the prediction of glass breakage. A theoretical method based on linear elastic fracture mechanics (LEFM) merged with approaches from stochastic geometry is used to predict the 2D-macro-scale fragmentation of glass. In order to predict the fragmentation of glass the 2D Voronoi tesselation of distributed points based on spatial point processes is used. However, for the distribution of the points influence parameters of the fracture structure are determined. The approach is based on two influencing parameters of fragment size delta and fracture intensity lambda , which are described in this paper. The Fragment Size Parameter describes the minimum distance between the points and thus the size of a fragment. It is derived from the range of influence of the remaining elastic strain energy in a single fragment taking into account the LEFM based on the energy criterion of Griffith. It considers the extent of the initial elastic strain energy U_0 before fragmentation obtained from the residual stress as well as a ratio of the released energy eta due to fragmentation. The Fracture Intensity Parameter describes the intensity of the fragment distribution, and thus the empirical reality of a fracture pattern. It can be obtained by statistical evaluation of the fracture pattern. In this work, the fracture intensity is determined from the experimental data of fracture tests. The intensity of a fracture is the quotient of the number of fragments in an observation field and its area and is assumed to be constant in the observation filed. The fracture intensity and the correlation between a constant intensity and the Fragment Size Parameter was determined. The presented methodology can also generally be used for the prediction of fracture patterns in brittle materials using a Voronoi tesselation over random fields.

Machining Distortion of Titanium Alloys Aero Engine Case Based on the Energy Principles

The simulation of a complete manufacturing process to produce an aero engine case, including forging, rolling, and machining processes, is analyzed via finite element software. The deformation of the turning and drilling processes is quantitatively studied using the energy principles. Firstly, simulations of multi-stage forging of aero engine case and machining-induced residual stress are conducted and verified via the residual stresses test in order to provide the initial elastic strain energy condition prior to machining processes. The effects of blank forging-induced residual stress and machining-induced residual stress on the deformation of titanium alloys aero engine case are investigated. Secondly, a potential energy expression for the machining processes is developed. The predicted results of turning and drilling simulations indicate that there is an optimal process in which the deformation and potential energy decline rapidly compared with the other processes and finally, gradually stabilize at the end of the process.

Oxidation Protection with Amorphous Surface Oxides: Thermodynamic Insights from Ab Initio Simulations on Aluminum.

Native surface films play a key role in the oxidation and corrosion protection of functional and structural materials. Here, we present a fully ab initio approach for understanding the thermodynamic driving force behind the initial phase selection among amorphous and crystalline structures for a surface film growing on a crystalline substrate. We apply the approach to elucidate the competition among corundum (α), spinel (γ), and amorphous (am.) Al2O3 films growing on aluminum metal. We show that the amorphous Al2O3 film becomes thermodynamically the most stable form below around ∼1 nm, that is, the relative energetic stabilities of thin polymorphic Al2O films follow am. < γ < α. As the film thickness increases, the relative stability relation first changes to γ < α < am. and then to the bulk limit of α < γ < am. The nanoscale γ films distort substantially to form exclusively four- and fivefold-coordinated Al-O polyhedra, lose the close-packed O framework, and become "amorphous-like", that is, exhibit both short-range order and energetic characteristics that are commensurate with the amorphous form. Our results provide a quantitative, first-principles confirmation for the early hypotheses on the thermodynamic stability of amorphous surface films and provide insights for the critical role they play in oxidation protection. Handling the complexities associated with the initial film growth, including bulk, surface, interface, and strain energy effects in realistically complex ab initio simulations, we expect this approach to contribute to understanding of the mechanism behind effective passivation films for aluminum alloys and beyond.

Comparison of three and four point bending evaluation of two adhesive bonding systems for glass-ceramic zirconia bi-layered ceramics

ObjectivesTo quantify the adhesion of two bonding approaches of zirconia to more aesthetic glass-ceramic materials using the Schwickerath (ISO 9693-2:2016) three point bend (3PB) [1] test to determine the fracture initiation strength and strain energy release rate associated with stable crack extension with this test and the Charalamabides et al. (1989) [2] four point bend (4PB) test. MethodsTwo glass-ceramic materials (VITABLOCS Triluxe forte, Vita Zahnfabrik, Germany and IPS.emax CAD, Ivoclar Vivadent, Liechtenstein) were bonded to sintered zirconia (VITA InCeram YZ). The former was resin bonded using a dual-cure composite resin (Panavia F 2.0, Kuraray Medical Inc., Osaka, Japan) following etching and silane conditioning, while the IPS.emax CAD was glass bonded (IPS e.max CAD Crystall/Connect) during crystallization of the IPS.emax CAD. Specimens (30) of the appropriate dimensions were fabricated for the Schwickerath 3PB and 4PB tests. Strength values were determined from crack initiation while strain energy release rate values were determined from the minima in the force-displacement curves with the 3PB test (Schneider and Swain, 2015) [3] and for 4PB test from the plateau region of stable crack extension. ResultsStrength values for the resin and glass bonded glass ceramics to zirconia were 22.20±6.72MPa and 27.02±3.49MPa respectively. The strain energy release rates for the two methods used were very similar and for the glass bonding, (4PB) 15.14±5.06N/m (or J/m2) and (3PB) 16.83±3.91N/m and resin bonding (4PB) 8.34±1.93N/m and (3PB) 8.44±2.81N/m respectively. The differences in strength and strain energy release rate for the two bonding approaches were statistically significant (p<0.05). SEM observations showed fracture occurred adhesively for the resin bonding and cohesively for the glass bonding. SignificanceThe present results indicate 3PB and 4PB tests have very similar values for the strain energy release rate determination. However while strength tests reveal minimal differences between resin and glass bonding, strain energy release rates for the latter are superior for bonding CAD/CAM milled glass-ceramics to zirconia.

Assessment of microcapsule—catalyst particles healing system in high performance fibre reinforced polymer composite

Autonomous self-healing in carbon fibre reinforced polymer (CFRP) is demonstrated using epoxy resin filled microcapsules and a solid-state catalyst. Microcapsules filled with oligomeric epoxy resin (20–450 μm) and particles of Sc(OTf)3 are embedded in an interleave region of a unidirectional CFRP laminate and tested under mode I loading. Double cantilever beam (DCB) test specimens containing variable concentrations of microcapsules and catalyst were prepared, tested and compared to those healed by manual injection with corresponding healing resin formulation. The healing efficiency was evaluated by comparing the maximum peak load recorded on load–displacement curves for pristine and healed specimens. A 44% maximum recovery was observed for specimens containing 10 wt% of solid phase catalyst and 11 wt% of epoxy microcapsules. However, a significant (80%) decrease in initial strain energy release rate (GIC) was observed for specimens with the embedded healing chemistries.

Bending strength of adhesive joints in microelectronic components: Comparison of edge-bonding and underfilling

The bending strength of underfilled and edge-bonded ball grid array (BGA) microelectronic packages assembled on printed circuit boards (PCBs) was compared using double cantilever beam (DCB) specimens. All specimens with fillets of the same size and shape failed at the same load, with cracks initiating and propagating within the PCB. This was consistent with measurements of the crack initiation strain energy release rate for PCB interfacial failure, which was significantly smaller than that of cohesive failure within the adhesives. Finite element analysis (FEA) indicated that the stress state in the PCB near the PCB-fillet interface in both underfilled and edge-bonded specimens was only a function of the adhesive fillet size and shape, and independent of the extent of the adhesive layer between the PCB and the BGA, and independent of the adhesive mechanical and thermal properties over the broad range of properties of the tested adhesives. This explained why decreasing the fillet curvature in edge-bonded specimens produced a significant increase in the joint strength. The crack path in the PCB of the edge-bonded specimens was found to change with the adhesive cure temperature; however, this had a negligible effect on the failure load.

Combined effect of strain-rate and mode-ratio on the fracture of lead-free solder joints

Abstract The critical strain energy release rate for the solder joint fracture was measured as a function of the strain rate and the mode ratio of loading. These data are useful in predicting the fracture of solder joints loaded under arbitrary combinations of tension and shear during the impact conditions typical of falling portable electronic devices. In this study, strain rates from quasi-static (close to 0 s − 1 ) to 61 s − 1 were investigated at phase angles from 0 to 60°, typical of the range found in microelectronic devices. Copper–solder–copper double cantilever beam (DCB) model specimens were prepared using SAC305 solder at cooling rates and times above liquidus typical of actual ball grid arrays (BGAs). A drop tester was designed and built to achieve different strain rates at various mode ratios. The critical initiation strain energy release rate, J ci , increased about 70% from quasi-static to intermediate strain rates, before decreasing by more than 67% from intermediate strain rates to 42 s − 1 .

Hot Deformation and Cracking during Compression of 21-4N Steel

Hot compressive deformation and cracking behaviors of cast 21-4N steel were investigated over a temperature range between 900°C~1250°C. The strength of the specimen at the outer surface of ingot is greater than that in the inner part because of the initial rapid solidification and corresponding fine structure at the outer surface. The initial flow stress hump in the stress-strain curves can be attributed to the dynamic recrystallization, which requires the initial strain energy build-up before the activation of grain nucleation process. With increase of temperature the critical stain for dynamic recrystallization decreases and at high enough temperatures, no critical strain for the build-up of strain energy is needed. At temperatures between 1000°C and 1200°C, homogeneous deformation occurred and no cracks were observed even after 50% strain. The cracks observed below 1000°C could be associated with the more difficult plastic flow in the presence of carbides and nitrides. The presence of fatal crack at 1250°C and the loss of hot ductility can be attributed to the partial melting in austenite grain boundaries at high temperatures.

Effect of Environmental Exposure on the Fracture Properties of an Epoxy Adhesive

An experimental study was carried out about the effect of warm moisture on the fracture energy of an adhesive system formed by steel adherends joined by an epoxy adhesive. The specimens were double cantilever beams, manufactured with the open-face technique. The halves of the specimens (single beams covered by the “primary” adhesive layer) were degraded in a climatic cell at 50°C and 100% RH, for time periods in the range of 1–5 weeks. At the end of each desired period, the half-specimens were dried, to account for irreversible effects only, and the bonds were completed with the second halves. Static fracture tests were carried out on an Instron 100 kN machine, monitoring crack propagation with a charge-coupled device microscope. The data were processed by means of the Simple Beam Theory to calculate the strain energy release rate and the R-curves were obtained. Similar trends were found for initial and steady critical strain energy release rates: compared to unexposed specimens, great part of the reduction (about −50%, −40%, respectively) occurred in the first week, stabilized values (about −80%, −60%) were observed after 3 weeks. The load-displacement curves decreased likewise. The fracture, mostly interfacial, followed a stepped crack path between the adherends.

Optimal Prestress Design and Construction Technique of Cable-Strut Tension Structures with Multi-Overall Selfstress Modes

This paper carries out investigations into the optimal prestress design and construction technique analysis of the cable-strut tension structure (CSTS) with multi-overall selfstress modes. First, the overall selfstress modes analysis method taking advantage of the symmetry of CSTS is proposed, which is applicable to CSTS with either single or multiple overall selfstress modes. Based on the selfstress modes analysis, the optimal prestress design of CSTS with multi-overall selfstress modes is then carried out and the minimum initial strain energy is selected as the objective function. After that, the construction technique using dynamic relaxation method is discussed, which is applicable not only to the final prestress stable systems but also to the in-slack cable-strut assemblies with insufficient number of structural members during the construction process. Finally, one laboratory model is designed to illustrate the proposed prestress design method and construction technique. The consistence of the measured values and computed results indicate the validity and accuracy of the proposed methods in this paper.

Effect of bud scars on the mechanical properties of Saccharomyces cerevisiae cell walls

To determine the effect of bud scars on the mechanical properties of the walls of Saccharomyces cerevisiae cells, freshly cultivated stationary phase cells stained with Alexa Fluor 488 conjugated wheat germ agglutinin were sorted according to the number of bud scars using fluorescence-activated cell sorting (FACS). The groups were daughter cells with no bud scars, and mother cells separated further by number of scars (one, two and more than two). Cells with more than three scars were very rare.Compression testing by micromanipulation was used to determine key mechanical properties of the sorted cells. For all cells the force and fractional deformation at bursting could be determined. For 69% of cells overall but only 32% of daughter cells, a large strain mathematical model using a linear elastic constitutive equation for the wall material could be fitted to force deformation data up to cell wall failure. For these cells, the wall surface modulus, elastic modulus, initial stretch ratio and strain energy per unit volume at bursting could be estimated. For the remainder of the cells, the lack of permanent deformation on repeated compression and release (at deformations not causing bursting) suggested the cell wall material was non-linear elastic but with no observable plastic behaviour.This is the first report to show directly that bud scars affect the global mechanical properties of yeast cells and that the important distinction with respect to scars is between daughter and mother cells. The former were smaller with more elastic walls and a higher mean initial stretch ratio. For cells for which the model could be fitted, the mean circumferential strain at bursting decreased with scarring (consistent with stiffer walls) whilst the stress increased. This may be due to the reported absence of chitin in the walls of daughter cells.

New Strain Energy–Based Coupled Elastoplastic Damage-Healing Formulations Accounting for Effect of Matric Suction during Earth-Moving Processes

AbstractInnovative initial elastic strain energy–based coupled elastoplastic hybrid isotropic damage and healing models for partially saturated soils have been developed and implemented for numerical simulation of two-dimensional earth-pushing processes. A class of elastoplastic constitutive damage-healing models, based on a continuum thermodynamic framework, is proposed within an initial elastic strain energy–based formulation. In particular, the change of effective stress caused by matric suction in the formulation is considered, and the governing incremental damage and healing evolutions are coupled and characterized through the effective stress concept in conjunction with the hypothesis of strain equivalence. Further, plastic flow is introduced by means of an additive split of the stress tensor. In this innovative formulation, two characteristic energy norms of the tensile and compressive strain tensors, respectively, are introduced for the corresponding damage and healing mechanisms. By incorporating...