Average Strain Energy Research Articles

Strain energy density approach for failure evaluation of occlusal loaded ceramic tooth crowns

The crown notch-like geometry creates a strong stress concentration, which is characterised by high stresses and severe stress gradient at the tip of the notch. In the vicinity of such stress concentrations the traditional approach based on a critical stress magnitude analysis may lead to unrealistic values for the critical load and failure conditions. At the same time, the crown geometry represents a relatively shallow rounded notch with the notch radius comparable with the tooth dimensions. Because of these geometrical features the popular approaches based on the critical stress gradient (notch stress intensity factor) could also lead to misleading results. Therefore, in this paper an alternative approach based on the averaged strain energy density over a defined volume is applied in order to predict and thus potentially avoid clinical failures in ceramic pre-molar tooth crowns. A two-dimensional finite element method is employed to investigate the stress state for various crown occlusal geometries, similar to those which were previously fabricated and subjected to mechanical testing. Then, the critical loads are calculated from the energy density approach and are compared with the results of an experimental study. The comparison of the predicted and calculated critical loads strongly supports the validity of strain energy density approach for failure assessment of tooth crown failures in the case of monotonic loading.

Slenderness ratio distribution and load-shortening behaviors of stiffened panels

This paper evaluates the distributions of three slenderness ratios of the plates, the stiffeners, and the stiffened panels, and presents a comparison of the load-shortening behaviors of the stiffened panels. The slenderness ratios, which represent the geometry and material properties of the stiffened panels, are obtained from deck and bottom platings of the midship area of 163 vessels, including 59 tankers, 46 bulkers, 28 product carriers, 15 container carriers, and 12 miscellaneous ships. Under the assumption that each slenderness ratio closely follows a normal distribution, average and upper/lower bound slenderness ratios are derived based on mean and mean plus/minus two times standard deviations. In order to compare the load-shortening capacities of the stiffened panels from simplified formulas of common structural rule (CSR) with those derived from a nonlinear FEA, a new parameter of relative average strain energy is introduced. It is concluded that the CSR formulas may be developed based on the very small initial imperfections of weld-induced initial deflection and residual stress.

Effect of the electrode particle shape in Li-ion battery on the mechanical degradation during charge–discharge cycling

The investigation addresses the effect of shape and aspect ratio, of typical electrode particles of Li-ion cell material, on the extent of fracture surface created due to intercalation-induced strain energy. Nodular, fibrous, and flaky-shaped particles were studied approximating them to sphere, cylinder, and disc geometries, respectively. Analytical expressions for stress distribution in slab and cylindrical-shaped particles were derived using thermal stress analogy. Such results are already available for spherical particles. Finite element study was carried out using COMSOL® Multiphysics package to complement the analytical work as well as for verification. The spatial and temporal variations of stresses and strain energy in the electrode particles of different shapes were established. Reportedly, solid electrolyte interphase formed on the fracture surface as well as the fracture-induced isolation of electrode material are the main causes of performance degradation and in this context, the intercalation-induced strain energy density becomes important. The sphericity of a particle, that is, the ratio of the surface area of a sphere to that of the particle of equal volume, was found to fittingly describe the effect of shape. The average strain energy density stored in a particle increases with the increasing sphericity. Therefore, fibrous and flaky-shaped particles are expected to have lower tendency for mechanical degradation than the nodular ones. The analysis is restricted only to the mechanics of mechanical degradation and not to the process or the chemistry point of view.

An experimental glenoid rim strain analysis for an improved reverse anatomy shoulder implant fixation

Loosening of glenoid components in TSA is a main cause of failure. In reverse anatomy TSA designs used for unstable joints, fixation is particularly demanding. Strains developed around the glenoid rim of biomechanical sawbone scapulae implanted with (a) the original fixed-fulcrum Bayley-Walker glenoid prosthesis in current clinical use, and (b) a revised version with conical cross-section, were compared. The conical shape of the revised design was hypothesized to produce greater strains in the glenoid rim than the original tapered screw design. The 2D strain field at three accessible locations around the rim of each scapula was measured with three-element rosette strain gauges for two types of simulated cancellous bone fill under applied physiologically relevant loads. The average strain energy densities around the rim for the conical design were greater than for the original design by a factor of 1.55-2.25 for all loading conditions. Results indicate that a significantly greater proportion of load was directed toward cortical bone in the conical design, thus promoting cortical bone loading.

Method of effective stress for fatigue: Part II – Applications to V-notches and seam welds

As shown in Part I of this paper, an effective stress method is specified by selecting a corresponding kernel G ( x , x ¯ ) defining the functional F . Among the numerous possibilities available only the stress averaging method by Neuber, which is broadly applied to the fatigue evaluation of seam welds, will be of the main concern of the present part. Based on the Neuber method, analytical expressions for the notch sensitivity coefficient and the effective stress are derived for V-notches where the approximate solutions both by Neuber and by Lazzarin et al. for the elastic stress field near the tip of a V-notch are used. Detailed comparisons with some empirical formulas like those of Peterson, Siebel and Stieler and still more are carried out. It reveals the necessity and the importance of the introduction of a consistency condition in case of small notch radii which has to be met by the notch sensitivity coefficient or the notch sensitivity in order to get physical meaningful effective stress also for sharp notches. The comparisons with the methods of the fictitious notch radius and the averaged strain energy, the first widely used in its worst case form by Radaj and the second conceived for sharp V-notches, both of practical relevance for the application to seam welds, are performed at length. Finally the analytical notch sensitivity coefficient is applied to steel and aluminium seam welds with failure both in toes, roots and ends of the welds by assuming different notch radii. For aluminium welds, the micro-structure length ρ ∗ is determined using the mathematical identification for the first time and the corresponding effective stress S–N curve is derived as well. The identified micro-structure length ρ ∗ = 0.21 mm for aluminium welds is two-thirds of that for steel welds ρ ∗ = 0.31 mm which is also identified in this paper and thus smaller than the popularly used ρ ∗ = 0.4 mm.

횡압력을 받는 실선 보강판의 평균압축강도

This paper presents estimation of average compressive strengths of three types of stiffened panels under lateral pressure and axial compression based on simplified formulas from CSRs and nonlinear FEAs. FEA scenarios are prepared based on the slenderness ratios of the stiffened panels used for in-service vessels. The seven step lateral pressures by 1bar increment are imposed on FE models assuming maximum 30m water height. The number of FEAs for FB-, AB-, and TB-stiffened panels is totally 189 times. FEA results show that existence of pressure can evolves significant reduction of ultimate strengths, meanwhile CSR formulas do not take into account the lateral pressure effect. Lateral pressure acting on the stiffened panel with higher column slenderness ratio more reduces the ultimate strengths than those with smaller column slenderness ratio. A new concept of relative average compressive strain energy instead of the ultimate strength is introduced in order to rationally compare the average compressive strength through complete compressive straining regime. The differences of the ultimate strengths between CSR formulas and FEA results are relatively small for FB- and AB-stiffened panels, but larger discrepancies of relative average compressive strain energies are shown.

조선 해양 구조물용 강재의 소성 및 파단 특성 III: 파단 변형률에 관한 실험적 연구

This is the third of several companion papers dealing with the derivation of material constants for ductile failure criteria under hydrostatic stress. It was observed that the ultimate engineering stresses and elongations at fracture from tensile tests for round specimens with various notch radii tended to increase and decrease, respectively, because of the stress triaxiality. The engineering stress curves from tests are compared with numerical simulation results, and it is proved that the curves from the two approaches very closely coincide. Failure strains are obtained from the equivalent plastic strain histories from numerical simulations at the time when the experimental engineering stress drops suddenly. After introducing the new concept of average stress triaxiality and accumulated average strain energy, the material constants of the Johnson-Cook failure criterion for critical energies of 100%, 50%, and 15% are presented. The experimental results obtained for EH-36 steel were in relatively good agreement with the 100% critical energy, whereas the literature states that aluminum fits with a 15% critical energy. Therefore, it is expected that a unified failure criterion for critical energy, which is available for most kinds of ductile materials, can be provided according to the used materials.

2 SMOOTH MUSCLE CELL APOPTOSIS PROMOTES VESSEL REMODELING, VIA ACTIVATION OF CELL MIGRATION, PROLIFERATION AND COLLAGEN SYNTHESIS

The applicability of the Averaged Strain Energy Density (ASED) criterion [1] to predict the failure of notched Polylactide Acid (PLA) specimens fabricated by Fused Deposition Modeling (FDM) is validated by means of experimental data reported by Ahmed and Susmel [2], Difficulties when estimating the ASED control volume radius based on the measured fracture toughness are revealed and discussed, whereas the accuracy of the ASED criterion is found to be satisfying when a novel alternative approach is used to define the control volume size.

Topology Optimization of Bracing Systems for Multistory Steel Frames under Earthquake Loads

Application of continuum structural topology optimization methods to the layout design of bracing systems for multistory steel frame buildings under earthquake loads is explored in this work. A weighted average strain energy sensitivity of element is formulated to be served as the element removal criterion in the optimization process, and then an ESO-based continuum structural topology optimization method for the layout design of multistory steel frame bracing systems subjected to earthquake-induced ground motions is presented. In each iterative design, an approximate reanalysis technique named CA method is adopted to reduce the computational effort. Finally, a design example is given to demonstrate the effectiveness of the presented optimization method for the optimal layout design of steel frame bracing systems under earthquake loads.

Micro-cracks informed damage models for brittle solids

A class of micro-cracks informed damage models for describing the softening behavior of brittle solids is proposed, in which damage evolution is treated as a consequence of micro-crack propagation. The homogenized stress–strain relation in the cracked microscopic cell defines the degradation tensor, which can be obtained by the equivalence between the averaged strain energy of the microscopic cell and the strain energy density of the homogenized material. This energy equivalence relationship serves as an energy bridging vehicle between the damaged continuum and the cracked microstructure. Several damage evolution equations are obtained by this energy bridging method. The size effect of the micro-cracks informed damage law is characterized through the microscopic cell analysis, and the proper scaling of the characterized damage evolution functions to eliminate mesh dependency in the continuum solution is introduced.

A general formulation of structural topology optimization for maximizing structural stiffness

This paper presents a general formulation of structural topology optimization for maximizing structure stiffness with mixed boundary conditions, i.e. with both external forces and prescribed non-zero displacement. In such formulation, the objective function is equal to work done by the given external forces minus work done by the reaction forces on prescribed non-zero displacement. When only one type of boundary condition is specified, it degenerates to the formulation of minimum structural compliance design (with external force) and maximum structural strain energy design (with prescribed non-zero displacement). However, regardless of boundary condition types, the sensitivity of such objective function with respect to artificial element density is always proportional to the negative of average strain energy density. We show that this formulation provides optimum design for both discrete and continuum structures.

Energy-based approach for the evaluation of low cycle fatigue behaviour of 2.25Cr–1Mo steel at elevated temperature

The energy-based approach for the evaluation of low cycle fatigue behaviour of 2.25Cr–1Mo steel at elevated temperature has been investigated and detailed analyses discussed. Plastic strain energy was determined per cycle and found to characterise both crack initiation and propagation to failure regimes. At cyclic stabilisation, average plastic strain energy may be used as a suitable damage parameter and correlations between experimental and predicted data determined. The fatigue toughness to failure of the material was established and the development of a fatigue toughness to crack propagation analysis is presented.

Hysteresis-loop representation for strain energy calculation and fatigue assessment

Improvements have been made to the cyclic strain energy density expression used in a fatigue life prediction method. The theory behind the prediction method is based on the understanding that the same amount of strain energy is dissipated during a monotonic fracture and a cyclic fatigue process. From this understanding, the failure cycle for a fatigue process can be determined by dividing monotonic strain energy by the average strain energy per cycle. Though this technique has been shown to be acceptable, it needs to be improved to account from the experimentally observed increase in the strain energy per cycle as the loading cycles approach fatigue. In order to improve the fatigue life prediction technique, experimental strain energy density per cycle is observed during the fatigue process of Aluminium 6061-T6 (Al 6061-T6) specimens. The results show exponential change in the strain energy density through the first 20 per cent and the last 30 per cent of the total failure cycles. The results lead to a new representation of strain energy density per cycle, which leads to an improved fatigue life prediction method. A comparison is made between the improved prediction method and experimental fatigue results. The comparison result validates the precision of the new hysteresis-loop representation.

Rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: Theoretical bases and applications

In the presence of sharp V-notches the stress distributions are singular and the intensity of the stress fields is given in terms of the notch stress intensity factors which are largely used in the literature for fatigue strength assessments of welded joints and other notched components. Very refined meshes are necessary to determine directly the NSIFs from the local stress distributions. Refined meshes are not necessary when the aim of the finite element analysis is to determine the mean value of the local strain energy density on a control volume surrounding the points of stress singularity. The SED in fact can be derived directly from nodal displacements, so that also coarse meshes are able to give sufficiently accurate values for it. The link between local SED and NSIFs is discussed with reference to some typical welded joints and to plates weakened by sharp V-notches. The SED-based procedure is found to be useful to determine theoretical stress concentration factors for holes and blunt U- and V-shaped notches.

Pseudo Strain Energy Density-Based Structural Damage Identification

In this paper, a new time-domain method for detecting structural local damage has been developed, which is based on the measured strain signals. The “pseudo strain energy density (PSED)” is defined and used to build two major damage indexes, the “average pseudo strain energy density” (APSED) and the “average pseudo strain energy density changing rate” (APSEDR). A probability and mathematical statistics technique is utilized to derive a standardized damage index. Afterwards, these indexes are used to establish the damage identification strategies for beam structures and plate structures respectively. Furthermore, the wavelet packet transform is used to pre-process the measured dynamic strain signals. Then, the effectivity of the new damage identification method is confirmed by numerical simulations. Finally, a laboratory beam model experiment is conducted to verify this method examine the feasibility and applicability of the new method.

Cyclic Stress Relaxation (Csr) of Filled Rubber and Rubber Components

Abstract Under repeated stressing it is well known that rubber materials exhibit cyclic stress relaxation (CSR). Previous work has shown that the amount of relaxation observed from cycle to cycle is significantly greater than that expected from static relaxation measurements. The reduction in the stress attained on the second and successive loading cycles as compared to the stress attained on the first cycle in a stress strain cyclic test of fixed amplitude has been measured for elastomer test pieces and engineering components. It is seen that the peak force, under cyclic testing to a specific maximum displacement, plotted against the number of cycles on logarithmic scales produces a straight line graph, whose slope correlates to the rate of cyclic stress relaxation per decade. The rate of cyclic stress relaxation was found to increase with displacement amplitude in all modes of deformation. Plotting the rate of stress relaxation per decade against the maximum average strain energy attained in the cycle reduces the data measured in different deformation modes for both simple test pieces and components to a single curve. This approach allows the cyclic stress relaxation in a real component to be predicted from simple laboratory tests.

Local fatigue strength parameters for welded joints based on strain energy density with inclusion of small-size notches

A fatigue strength parameter for (seam-)welded joints is presented which is based on the averaged elastic strain energy density (SED) criterion applied to full circle and semicircular ‘control volumes’, the latter centred by the expected crack path. The parameter is applicable both at weld toes and weld roots, at least in the medium-cycle and high-cycle fatigue range where elastic conditions are prevailing. Based on a rectangular slit-plate model representing the weld root and analysed by the finite element method, the effect of the following influencing conditions is investigated: tension loading (mode 1) and shear loading (mode 2), slit-parallel tension loading acting on a rounded slit tip, pointed slit tip versus small-size key-hole at the slit tip, semicircle and narrow sector versus full circle or full sector SED evaluations, distortional SED versus total SED under plane strain conditions. The following conclusions are drawn from the numerical results. The SED approach should be based on the full circle or full sector evaluation of the total SED, with R 0 = 0.28 mm for steels. In cases of a markedly unilateral angular SED distribution, the semicircle evaluation centred by the expected crack path is more appropriate. The use of small-size reference notches instead of pointed notches provides no advantage. The endurable remote stresses for fatigue-loaded welded joints according to the SED approach are well in correspondence with those according to the fictitious notch rounding approach. High accuracy of the results can already be achieved with a rough meshing at the pointed notches.

A generalised notch stress intensity factor for U-notched components loaded under mixed mode

A novel notch stress intensity factor (NSIF) for U-notched specimens loaded under mixed mode is examined in this article. The concept is based on the averaged strain energy density criterion, or alternatively on the cohesive zone model, as well as the equivalent local mode approach. To a certain extent, it is a generalisation of Glinka’s NSIF for mode I, where σ tip is replaced by σ max. The applicability of a fracture criterion based on this new NSIF is checked against 171 fracture tests with PMMA (at −60 °C) performed on U-notched specimens, with different notch root radii and loaded under mixed mode. The asymptotic behaviour of the new NSIF as the notch becomes a crack (when the notch root radius tends to zero) or when the notch disappears (when the notch root radius tends to infinity) is also discussed.

Structural Factors That Mediate Scleral Stiffness

The intent of this study was to correlate measures of structurally relevant biochemical constituents with tensile mechanical behavior in porcine and human posterior sclera. Posterior scleral strips 6 x 25 mm were harvested from 13 young porcine and 10 aged human eyes and stored frozen at -20 degrees C. Mechanical hysteresis from 10 consecutive load cycles to a peak stress of 1.0 MPa was recorded via a custom-built soft tissue tester. In a parallel study, tissue adjacent to the mechanical test specimens was apportioned for each of five assays measuring: total collagen content, nonenzymatic cross-link density, elastin content, glycosaminoglycan content, and water content. The average porcine scleral modulus at 1% strain was 75% less than that measured for human tissue (0.65 +/- 0.53 MPa versus 2.60 +/- 2.13 MPa, respectively; P < 0.05). However, the average strain energy absorbed per loading cycle was similar (6.09 +/- 2.54 kJ/m(3) vs. 5.96 +/- 2.69 kJ/m(3) for porcine and human sclera respectively; P > 0.05). Aged human sclera had relatively high fluorescence due to nonenzymatic cross-link density (2200 +/- 368 vs. 842 +/- 342; P < 0.05) and low hydroxyproline content (0.79 +/- 0.17 microL/mL/g versus 1.21 +/- 0.09 microL/mL/g; P < 0.05) while other measured biochemical factors were statistically similar (P > 0.05). Aged human tissue had superior mechanical stiffness despite reduced collagen content, partially because of the accumulation of nonenzymatic cross-links. Differences in collagen content and cross-link density either had no effect or offsetting effects on the ability of the tissues to absorb strain energy.

Fracture assessment of U-notches under mixed mode loading: two procedures based on the ‘equivalent local mode I’ concept

Two fracture criteria are proposed and applied to blunt-notched components made of brittle materials loaded under mixed mode; the former is based on the averaged strain energy density over a given control volume, the latter on the cohesive crack zone model. In both instances use of the equivalent local mode I hypothesis is made. Only two material properties are needed: the ultimate tensile strength and the fracture toughness. Numerical predictions of rupture loads from the two criteria are compared with experimental measurements from more than 160 static tests with notched beams. The samples are made of PMMA and tested at − 60°C to assure a bulk behaviour almost linear elastic up to rupture. Notch root radii range from 0.2 to 4.0 mm and load mixicity varies from pure mode I to a prevailing mode II. The good agreement between theory and experimental results adds further confidence to the proposed fracture criteria.