Change In Strain Energy Research Articles

Improved Damage Quantification from Elemental Modal Strain Energy Change

An improved structural damage quantification algorithm is presented based on the elemental modal strain energy change before and after the occurrence of damage in a structure. The algorithm include...

Closure to “Structural Damage Detection from Modal Strain Energy Change” by Z. Y. Shi, S. S. Law, and L. M. Zhang

Closure to “Structural Damage Detection from Modal Strain Energy Change” by Z. Y. Shi, S. S. Law, and L. M. Zhang

Discussion of “Structural Damage Detection from Modal Strain Energy Change” by Z. Y. Shi, S. S. Law, and L. M. Zhang

Discussion of “Structural Damage Detection from Modal Strain Energy Change” by Z. Y. Shi, S. S. Law, and L. M. Zhang

Selection and change in deformation mode to maintain continuity of strains and slip/twinning planes at lamellar boundaries in fatigued TiAl polysynthetically twinned crystals

Change in deformation mode in six types of γ domain (AM–CT) and α2 plates in TiAl polysynthetically twinned (PST) crystals fatigued at a loading axis parallel to lamellar planes with stress amplitude (Δσ) of 420–450 MPa was examined by the transmission electron microscope focusing on continuity of macroscopic strains and slip/twinning planes at lamellar boundaries. At Δσ = 420 and 450 MPa, the strain continuity is always maintained at lamellar boundaries by activation of one of the symmetric twinning systems in A-type domain and selection of the dominant deformation mode between ordinary dislocations and twins in (B and C)-type γ domain. The (B and C)-type γ domains of BM,BT,CM and CT behave as two sets of (BM,CT) and (BT,CM) because each set selects either the deformation mode of ordinary dislocations or twins as a dominant system in order to keep macroscopic strain continuity. The set (BT,CM) which accounts for a larger volume fraction than the set (BM,CT) in TiAl-PST crystals used in this study selected a twinning system at Δσ = 450 MPa, while ordinary dislocations were selected at Δσ = 420 MPa. At Δσ = 450 MPa, twinning deformation prevented the further motion of ordinary dislocations with a Burgers vector parallel to lamellar boundaries, and rapid fatigue hardening occurred accompanied by reduction of the accumulative plastic strain energy. Anomalous change in strain energy during fatigue is infiuenced by the volume fraction of a set of (B and C)-type domain and the anomalous behavior in fatigued TiAl-PST crystals may disappear when each type of γ domain is equally distributed.

Thermo-oxidative aging and fatigue behavior of dynamically vulcanized PVC/ENR thermoplastic elastomers

Dynamically vulcanized poly(vinyl chloride)/epoxidized natural rubber (PVC/ENR) thermoplastic elastomers (TPEs) were prepared following a semi-efficient vulcanization system (semi-EV) with the incorporation of di-ethylhexyl phthalate (DOP) as a plasticizer. The PVC/ENR TPEs were melt mixed at 150°C and 50 rpm using a Brabender Plasticorder. The effect of dynamic curing on the fatigue behavior of the PVC/ENR TPEs was investigated. The properties investigated include fatigue life, stress - strain behavior, strain energy, morphology, and the effect of hysteresis. The unaged samples showed that as the sulfur concentration increases the fatigue life increases which could be related to the increase in cross-link density as indicated from the swelling index data. The increase in cross-link density increases the resistance of these materials against external dynamic stress. Hysteresis study revealed that samples with higher sulfur concentration are less sensitive towards changes in strain energy. As a result they exhibited lower heat build-up and consequently higher fatigue life. The effect of thermo-oxidative aging (TOA) on the fatigue behavior was investigated by exposing the PVC/ENR TPEs in an air oven at 80°C for 168 hours. It was found that all the properties studied decreased after thermo-oxidative aging process. This suggests that some micro-structural changes such as the formation of new cross-links due to post curing has taken place. This accounts for the reduced fatigue life and resilience while hysteresis, modulus, and hardness increased.

Reactions of mono- and bimolecular hydrogen transfer in alkyl radicals: analysis using the parabolic model and density functional calculations

Experimental data on monomolecular hydrogen transfer in the reactions of the type RC·H(CH2)nCH2R1 → RCH2(CH2)nC·HR1 (n = 2—4, R and R1 are alkyl substituents) were analyzed using the parabolic model (PM). The parameters characterizing this class of reactions were calculated. Isomerization of alkyl radicals via cyclic transition states (TS) is characterized by the following energy barriers to thermoneutral reaction Ee0: 53.5, 65.4, and 63.2 kJ mol–1 for the six-, five-, and seven-membered TS, respectively. The Ee0 energy and the strain energy change in parallel in the series of cycloparaffins CnH2n. Density functional calculations of intramolecular hydrogen transfer in the n-butyl and n-pentyl radicals and of the bimolecular hydrogen abstraction from the ethane molecule by the ethyl radical were performed. The activation energies of the intra- and intermolecular hydrogen transfer were compared. The parameters of the PM were compared with the interatomic distances in the reaction center of the TS calculated by the density functional method.

An effective inclusion model for effective moduli of heterogeneous materials with ellipsoidal inhomogeneities

In the present study, an effective inclusion model for effective elastic moduli of heterogeneous materials is proposed to analyze the problem of an infinite matrix containing an ellipsoidal RVE. It is assumed that the strain energy changes of the infinite matrix due to embedding the RVE and its effective inclusion into the matrix are identical. A system of equations for effective moduli is then formulated using the new energy balance equation that interrelate effective moduli to a problem of an infinite matrix containing N inhomogeneities in an ellipsoidal sub-region. A generalized non-interacting solution derived based on the present formulation coincides with the estimates of the Hashin–Shtrikman type obtained by Ponte Casta ñ eda and Willis [J. Mech. Phys. Solids 43 (1995) 1919]. The effect of the shapes of RVEs on the approximate solution is also discussed in detail. As further application of the present formulation, the numerical models for the effective moduli of solids with cracks and heterogeneous materials with spherical inhomogeneities are proposed, which account for the interactions among many cracks or spherical inhomogeneities. The numerical results are then compared with the existing micromechanics models and experimental data.

Evolution and analysis of γ′ rafting during creep of single crystal nickel base superalloy

By means of TEM observation and finite element analysis, an investigation has been made into the directional coarsening of the γ′ phase for a single crystal nickel base superalloy with [001] orientation during creep at 1040°C. The results show that the strain energy change related to the elastic strain is to be the driving force for γ′ rafting. The extruded strain of the lattice in the cuboidal γ′ interfaces results in a supersaturation of the elements Ta and Al of larger atomic radius. The extrusion or expansion strain in the lattice of the cuboidal γ′ planes may repel or trap these atoms to promote the directional growth of the γ′ phase into a needle-like raft structure along the direction parallel to the stress axis under an applied compression stress, or into a meshlike raft structure along the direction perpendicular to stress axis under applied tensile stress. The normal direction of the expanding lattice is supposed to be the one in which the γ′ rafts grow. The rate of γ′ rafting is enhanced by increasing viscoplastic flow in the γ matrix and elastic strain in the γ′ phase. Therefore, there is a smaller rate of growth under compressive than under tensile stress as a result of the smaller expansion strain and viscoplastic flow occurring in the former.

Critical thickness of an epilayer grown on a finite substrate with different elastic constants

This study addresses the problem of the critical thickness of an epilayer grown on a finite substrate with different elastic constants. The principle of superposition and Fourier integral methodology are used to solve the displacement and stress fields that satisfy the boundary conditions. The change in strain energy caused by the introduction of a misfit dislocation is defined as the dislocation formation energy E f. Meanwhile, the epilayer thickness, corresponding to E f=0, is the epilayer critical thickness h c. This investigation reveals a promising characteristic of using a thin substrate, namely that when the substrate is very thin and the shear modulus ratio of epilayer over substrate is 1/10, then if the corresponding h c is smaller than the substrate thickness, h c will decrease as the shear modulus ratio increases. However, if the corresponding h c is greater than the substrate thickness, h c markedly increases with an increase of the shear modulus ratio, becoming infinite. When the substrate is very thin, the h c also increases rapidly with the epilayer (substrate) Poisson ratio and finally reaches infinity; however, the pattern differs from that of the variation in the ratio of the shear modulus. If the substrate becomes thinner and transforms into a diaphragm structure, the epilayer critical thickness reaches infinity, regardless of the magnitude of the shear modulus ratio, epilayer, and substrate Poisson ratio. Results obtained when the epilayer and substrate share identical elastic constants are compared with those of Zhang et al. and Fruend and Nix. The present result lies between those obtained in these two earlier studies.

Application of Dynamic System Identification to Timber Beams. I

In this first part of a two-part paper, development of a method of dynamic system identification for timber beams is presented with an analytical verification of the method using a finite-element model. A method of global nondestructive evaluation for identifying local damage and decay in timber beams is investigated in this paper. Experimental modal analysis is used in conjunction with a previously developed damage localization algorithm. The damage localization algorithm utilizes changes in modal strain energy between the mode shapes of a calibrated model, representing the undamaged state of the beam of interest, and the experimentally obtained mode shapes for a timber beam. Analytical evaluations were performed to demonstrate and verify the use of this method of global nondestructive evaluation for the localization of damage or decay in timber beams. In a companion paper, experimental laboratory tests are presented that verify the use of dynamic system identification to locate damage within timber beams.

Application of Dynamic System Identification to Timber Bridges

A method of global nondestructive evaluation for identifying local damage and decay in timber beams was developed in previous analytical studies and verified experimentally using simply supported beams in the laboratory. The method employs experimental modal analysis and an algorithm that monitors changes in modal strain energy between the mode shapes of a damaged structure with respect to the undamaged structure. A simple three-girder bridge was built and tested in a laboratory to investigate the capability and limitations of the method for detecting damage in a multimember timber structure. The laboratory tests showed that the method can correctly detect and locate a simulated pocket of decay inflicted at the end of a girder as well as detect a notch removed from the midspan of a girder. The tests showed that the method can correctly detect damage simultaneously at two locations within the bridge, but also that large magnitudes of damage at one location can mask smaller magnitudes of damage at another location. When a calibrated baseline model is used to represent the undamaged state of the bridge, the results show that the method of nondestructive evaluation is able to detect each case of inflicted damage, but with some increase in localization error.

Rotamer strain energy in protein helices - quantification of a major force opposing protein folding

It is widely believed that the dominant force opposing protein folding is the entropic cost of restricting internal rotations. The energetic changes from restricting side-chain torsional motion are more complex than simply a loss of conformational entropy, however. A second force opposing protein folding arises when a side-chain in the folded state is not in its lowest-energy rotamer, giving rotameric strain. χ strain energy results from a dihedral angle being shifted from the most stable conformation of a rotamer when a protein folds. We calculated the energy of a side-chain as a function of its dihedral angles in a poly(Ala) helix. Using these energy profiles, we quantify conformational entropy, rotameric strain energy and χ strain energy for all 17 amino acid residues with side-chains in α-helices. We can calculate these terms for any amino acid in a helix interior in a protein, as a function of its side-chain dihedral angles, and have implemented this algorithm on a web page. The mean change in rotameric strain energy on folding is 0.42 kcal mol −1 per residue and the mean χ strain energy is 0.64 kcal mol −1 per residue. Loss of conformational entropy opposes folding by a mean of 1.1 kcal mol −1 per residue, and the mean total force opposing restricting a side-chain into a helix is 2.2 kcal mol −1. Conformational entropy estimates alone therefore greatly underestimate the forces opposing protein folding. The introduction of strain when a protein folds should not be neglected when attempting to quantify the balance of forces affecting protein stability. Consideration of rotameric strain energy may help the use of rotamer libraries in protein design and rationalise the effects of mutations where side-chain conformations change.

Structural Damage Detection from Modal Strain Energy Change

A structural damage detection method based on modal strain energy (MSE) change before and after damage is presented in this paper. The localization of damage based on MSE of each structural element is briefly presented, and the sensitivity of the MSE with respect to a damage is derived. The sensitivity is not based on any series expansion and is a function of the analytical mode shape changes and the stiffness matrix. Only incomplete measured mode shapes and analytical system matrices are required in this damage localization and quantification approach. Results from a numerical example and an experiment on a single-bay, two-story portal steel frame structure are investigated. The effects of measurement noise and truncated analytical mode shapes are discussed. Results indicate that the proposed approach is noise sensitive, but it can localize single and multiple damages. Damage quantification of two damages is successful with a maximum of 14% error under a 5% measurement noise.

A molecular mechanics study of 1:1 complexes between azobenzene derivatives and β-cyclodextrin

Azobenzene derivatives in solution present thermal cis–trans isomerization through the double bond –NN–. Experimental results showed that β-cyclodextrin inhibited the isomerization process for some azoderivatives while others were not affected. As previous model studies on the inclusion complexation of cyclodextrins with various guests, offered significant insights into the non-covalent intermolecular interactions and theoretical calculations helped to illustrate the driving forces for the complexation, here we have undertaken a theoretical study of the entire process of the formation of 1:1 stoichiometry azobenzene/β-cyclodextrin structures, in order to contribute to the understanding and rationalization of the experimental results reported before. With this purpose, we first searched for a possible way of formation of each substituted azobenzene/β-cyclodextrin inclusion complex and then we have performed an analysis of the strain energy changes involved and we have also analyzed the interaction forces driving towards the different kinds of stable structures yielded by the calculation procedure.

STRAIN ENERGY ASSOCIATED WITH STRUCTURAL MODIFICATIONS

Modifications to linear elastic structures are considered for which the amount of additional stiffening material is increased proportionally. It is proved that, for fixed loading, the strain energy will not be increased and, for fixed displacements, the strain energy will not be decreased by the addition. Furthermore the graphs of strain energy versus the amount of additional material will be monotonic. Also the strain energy absorbed by an incremental amount of additional material must equal the change in the total strain energy for both the cases of fixed loading and fixed displacements. These behavioural properties have been formulated as three theorems. The paper justifies and discusses these and presents some simple illustrations.

Oil palm wood flour filled natural rubber composites: fatigue and hysteresis behaviour

The fatigue and hysteresis behaviour of oil palm wood flour (OPWF) filled natural rubber composites was studied. The stress at any strain decreased with increasing OPWF loading in the composites. As the filler loading increased, the poor wetting of the OPWF by the rubber matrix gave rise to poor interfacial adhesion between the filler and rubber matrix. Results also indicate that the composite with the highest loading of OPWF was the most sensitive towards changes in strain energy, and hence exhibited the highest hysteresis. Thermal ageing not only reduced the fatigue life, but also increased the hysteresis of the composites. © 2000 Society of Chemical Industry

Coherency Strain and a New Yield Criterion

ABSTRACTWe have studied the onset of plasticity in coherently-strained semiconductor superlattices, using nano-indentation with spherical indenter tips to observe the full stress-strain curve. The yield pressure is reduced by as much as a factor of two by the presence of the coherency strain. By varying the thicknesses and strains of the superlattice layers, we provide a proof that yield commences over a finite volume. It is properties averaged or summed over this volume which determine the yield pressure. We show that the relevant yield criterion for our experimental data is the rate of change of elastic strain energy with plastic relaxation, integrated over a volume of the order of a micron across. This result is expected to be valid for other systems with highly inhomogenous strain fields, and hence to be applicable to modelling of point contact, and to the design and understanding of structural materials which have coherently-strained microstructure.

Inelastic Effects of Microcracking: A New Continuum Damage Model

Microcracking is an important mechanism of damage accumulation in stressed solids. Two contributions to deformation can be distinguished: modification of the bulk effective elastic behaviour as cracks are introduced; and accumulation of an inelastic offset for each crack on formation. Equivalent medium approximations consider the former. In this study we have developed a new formulation to model the latter. The change in strain energy at the instant of formation of each individual microcrack is used to calculate the incremental inelastic strain increase during monotonic loading. This leads to integral equations describing the damage state, in which stress and strain are functions of damage. The macroscopic behaviour is path dependent. We obtain an explicit form of the stress-strain relation as a function of both intrinsic and extrinsic variables (damage and loading history) in order to test the model using experimental data for uniaxial tests on rock samples. Quantitative damage estimation is made through monitoring acoustic emissions emitted as microcracks form, which are related to crack dimensions through an independently determined scaling relation. The new model successfully reproduces the experimental stress-strain behaviour through failure, and also allows secondary effects, such as residual strain or hysteresis to be modelled, which is not possible with the equivalent elastic medium approach. The results suggest that (a) the incremental damage approach is needed to fully model behaviour in compression; (b) inelastic effects arising from cracking must be considered as well as modifications to the sample stiffness; and (c) acoustic emission parameters can be used in quantitative modelling of inelastic behaviour of cracked solids.

四点曲げ試験によるぜい性コーティング皮膜のはく離強度評価

In order to evaluate the delamination strength of brittle coating on ductile substrate, the four-point bending test method was proposed by expanding the tensile test method. The delamination energy was derived as a function of bending moment, curvature of specimen at delamination of coating and material's constants by theoretical analysis where the change of strain energy both in coating and substrate at delamination were considered. The method was applied to the specimen with WC-Co coating on an annealed tool steel prepared by high-velocity flame spraying. With increasing bending moment, the coating is divided repeatedly by cracks with almost the same interval. The crack interval at the delamination increases and the delamination energy of coating decreases with an increase in coating thickness. The four-point bending method is also effective to evaluate the delamination strength of brittle coating.

STRUCTURAL DAMAGE LOCALIZATION FROM MODAL STRAIN ENERGY CHANGE

A method based on modal strain energy is presented for locating damage in a structure. This method makes use of the change of modal strain energy in each structural element before and after the occurrence of damage. Some properties of this Modal Strain Energy Change are given to illustrate its sensitivity in locating the structural damage. Information required in the identification are the measured mode shapes and elemental stiffness matrix only without knowledge of the complete stiffness and mass matrices of the structure. Several damage cases in a simulated structure are studied in which the effect of random error in terms of measurement noise in the mode shapes and systematic error in terms of errors from incomplete measurements are considered. This method is then applied to detect damage in a single-bay two-storey portal steel frame structure. Results illustrate that the MSEC is sensitive to damage, and the proposed method is simple and robust in locating single or multiple damages in a structure.