Shear Strain Energy Research Articles

Online multiaxial fatigue damage evaluation method by real‐time cycle counting and energy‐based critical plane criterion

AbstractTo realize online multiaxial fatigue damage assessment for the mechanical components in service, an online multiaxial cycle counting method is proposed coupled with the segment processing technique and Wang‐Brow's relative equivalent strain concept. Meanwhile, considering all the stress and strain components, which contribute to the fatigue damage on the critical plane, a multiaxial fatigue damage model without any weight coefficients is also proposed in an equivalent form of shear strain energy. Then, an online fatigue damage evaluation method for multiaxial random loading is developed by combining with the proposed damage model and online cycle counting method. The experimental results showed that the proposed online cycle counting method can be successfully applied to the calculation of multiaxial fatigue damage under random loading. Moreover, the proposed online multiaxial fatigue damage evaluation method can provide satisfactory predictions.

Multiaxial Fatigue and Cracking Orientation of Forged AZ80 Magnesium Alloy

The effect of the multiaxiality and proportionality of loading on the cyclic behaviour and early cracking behaviour was studied for closed die forged AZ80 Mg alloy. Several different loading paths were presented, uniaxial and biaxial with varying levels of non-proportionality. In multiaxial loading the effect of proportionality is only present on the shear response of the material and increasing levels of non-proportionality is detrimental to the fatigue life. When compared with proportional loading, a 50% reduction in life was observed under 90° out of phase non-proportional loading. The pure axial cracking behaviour is dominated by transverse cracks along the plane of maximum normal stress, whereas in pure shear the material exhibited longitudinal cracking (shear dominated) behaviour in LCF regime and helical cracking (normal stress dominated) in the HCF regime. The synergistic effects of each individual uniaxial cracking modes contribution towards the combined macroscopic cracking behaviour in multiaxial loading was investigated, and was dominated by transverse cracking when the shear strain energy density (SED) contribution to the total SED was low, and mixed cracking when the shear SED contribution was high.

Equivalent energy-based critical plane fatigue damage parameter for multiaxial LCF under variable amplitude loading

Combining the concept of energy on the critical plane, a multiaxial fatigue damage parameter without any weight coefficient was proposed and the effects of non-proportional additional hardening and mean stress on fatigue damage can be reflected more perfectly using an equivalent form of shear strain energy. Furthermore, two sets of experimental data are employed to verify the proposed method, and the sensitiveness to fatigue life of the proposed equivalent stress correction factor is discussed as well. The results show that satisfactory and conservative assessments can be obtained by the proposed method, especially under multiaxial irregular loading with great randomness.

Physical interpretation of moment tensor and the energetics of shear faulting

Moment tensor is a basic concept of source representation in seismology, established in the 1970s. On the basis of theoretical consideration to the equation of motion in continuum mechanics, we clarified the physical meaning of the Backus-Mulcahy moment tensor and derived a fundamental equation that the moment tensor of a seismic event is mathematically equivalent to the volume integral of coseismic static stress changes over the whole region. This equation provides new perspectives on the interaction between the inelastic source process and the elastic process in the surrounding region. As an example, we applied it to the energetics of shear faulting and obtained a quantitative relation between the work done for shear faulting and the static change in elastic strain energy in the surrounding region. With this energy equation, we elucidated the theoretical background of the Wallace-Bott hypothesis; that is, when the level of background tectonic stress is much higher than coseismic stress changes, the most probable orientation of slip on a given fault is parallel to the maximum resolved shear stress there in the sense of the efficiency of shear-strain energy release in the surrounding region.

Parametric study of a fibrous energy absorbing material under impact shear loading

A comprehensive experimental impact characterization study of novel impact energy absorbing (IEA) materials under impact shear loading is conducted. Electro-flocking process is employed to fabricate the novel fiber based padding materials, also known as flocked energy absorbing materials (FEAM). FEAM IEA panels are prepared by flocking 1–3 mm long, 6–60 denier nylon fibers onto a planar polyester fabric sheet. The impact energy absorption under combined pre-compression loading and shear impact loading is investigated using a custom built guided weight drop tower along with a specially designed pre-compression and shear loading fixture for this study. A parametric study is performed where the effect of fiber material properties such as flock fiber length, diameter and flock density (number of flock fibers per area) on IEA is investigated and they are later compared with that of Vinyl Nitrile (VN) foam materials. Padding material based on FEAM configurations showed remarkable improvement when compared directly to VN foam with a 135% increase in shear strain energy density for the high impact velocity loading condition. Additionally, for low velocity impact conditions, the FEAM based padding materials out performed with a 49% increase in shear strain energy density as compared to VN foam.

Investigation on shear strain of reinforced concrete membrane panels subjected to pure shear

Hsu recently conducted a shear test on nine reinforced concrete panel elements subjected to applying pure shear using a shear testing device. Modern truss models (i.e. modified compression field theory and a rotating angle softened truss model) are used to perform a complex nonlinear analysis through a trial and error method based on a double loop. This analysis is conducted by employing equilibrium conditions, compatibility conditions, and a ductile stress–strain relationship of a reinforced concrete membrane panel in a biaxial state. In this study, an effective algorithm that uses a revised Mohr compatibility method based on the failure criteria of struts and ties is proposed. This algorithm is used to improve the convergence rate in the analysis of shear history, which was performed in the experiment of Hsu. The result of the analysis indicates that the shear strain energy in a state of extended shear strain is influenced by the relationship between principal compressive stress and strain (crushing failure).

Use of an energy‐based/critical plane model to assess fatigue life under low‐cycle multiaxial cycles

AbstractFor engineering components subjected to multiaxial loading, fatigue life prediction is crucial for guaranteeing their structural security and economic feasibility. In this respect, energy‐based models, integrating the stress and strain components, are widely used because of their availability in fatigue prediction. Through employing the plastic strain energy concept and critical plane approach, a new energy‐based model is proposed in this paper to evaluate the low‐cycle fatigue life, in which the critical plane is defined as the maximum damage plane. In the proposed model, a newly defined NP factor κ* is used to quantify the nonproportional (NP) effect so that the damage parameter can be conveniently calculated. Moreover, a simple estimation method of weight coefficient is developed, which can reflect different contributions of shear and normal plastic strain energy on total fatigue damage. Experimental data of 10 kinds of materials are employed to assess the effectiveness of this model as well as three other energy‐based models.

Low-cycle multiaxial fatigue behavior and life prediction of Q235B steel welded material

Low-cycle torsional and multiaxial fatigue experiments are carried out for thin-walled Q235B steel welded specimens under both in-phase and 90° out-of-phase loading paths. A remarkable non-proportional additional hardening effect exists in the Q235B steel welded material under the 90° out-of-phase loading paths. A new energy-based fatigue parameter is proposed that incorporates the shear strain energy on the weighted critical plane and the normal strain energy on both the weighted critical plane and orthogonal plane. The proposed energy-based fatigue parameter provides a superior ability to make life prediction for the Q235B steel welded material under the torsional and multiaxial loading paths.

Effect of liquefaction on nonlinear seismic response in layered soils: a case study of Babol, North of Iran

Soft soil layer can significantly increase destruction during ground motions. Although, earthquake waves pass through mainly rocky media to reach ground surface, they often transit through a thin layer of surficial soil which can dramatically affect ground surface motions. This study thoroughly investigates the effect of liquefaction on the seismic response of soft soil layers using the finite difference method in specific areas of Babol City, north of Iran. Nonlinear effective stress analysis was carried out using FLAC 2 D, a finite difference based software. Liquefaction potential was evaluated based on both pore pressure ratio (R u) and shear strain amplitude criteria. The logical agreement of these two criteria was observed. Based on the results, near the river of this city, strong site effect observed due to the presence of soft soil layers and liquefaction, effectively altered the amplitude and frequency content of ground motions. Seismic analyses proved that spectral acceleration responses were attenuated for low periods due to the shear strain development and energy dissipation of motion but they increased for longer periods, which could strongly affect the seismic design of structures.

Experimental and theoretical study on energy convergence characteristics of adiabatic shear fracture process in high-speed machining of hardened stainless steel

The formation of isolated segment chip due to the occurrence of adiabatic shear fracture (ASF) in adiabatic shear band (ASB) is a significant phenomenon under the high cutting speed. In the present work, the experimental and theoretical methods were adopted to further investigate the energy convergence characteristics in ASB during ASF process in high-speed machining. A hardened stainless steel used in turbine blade was selected as the workpiece. The chip morphology transformation from serrated chip to isolated segment chip was obtained through the high-speed machining experiment. The ductile crack propagation in ASB was observed microscopically. The relations of serrated segment geometry with the cutting conditions were revealed experimentally. According to the continuum governing equations and the deformation and energy analytical models, the distributions of shear velocity, shear strain rate, shear strain, and shear energy in ASB under various cutting speeds and feeds were analyzed combining with the constitutive and stress relations. The energy convergence characteristics in ASB during ASF process with the change of cutting conditions were analyzed and discussed. The results showed that the austenite blocks in the hardened stainless steel influenced the crack propagation in ASB. The larger shear strain induced thinner ASB would accelerate the thermal softening and strain localizing effects, resulting in severer energy convergence in ASB. The energy convergence was uniformly distributed and always kept a constant limit value in the whole ASB when ASF occurred.

Experimental studies of short concrete reinforced steel fiber beams under bending

Abstract This paper presents the results of a test program on 24 concrete beams with a cross section of 15 x 15 cm. Those are divided into two groups of 12 beams. Group I has a steel fiber content of 40 kg/m³ while Group II uses 60 kg/m³ of steel fibers. The tests consider three sets of beam lengths: 300 mm, 500 mm and 800 mm. The beams were submitted to bending aiming at investigating shear stresses, bending, strain energy, toughness, scale effect and fracture energy. Group II showed a slightly higher resistance to rupture than Group I. However, the smaller the length, the larger the influence of the fiber content. The largest fiber content gave the concrete higher resistance when submitted to bending and shear, especially for the smaller lengths. Both strain and fracture energy, however, show considerable differences for smaller lengths, but are almost the same for the 800 mm beams. Toughness shows improvement in the longer beams and a reduction of this property in the shorter beam from Group II.

Fatigue life prediction for metals using an improved strain energy density model

An improved strain energy density model is proposed on the basis of critical plane concept to better predict the multiaxial fatigue life of metals, especially during nonproportional loadings. This approach is based on the normal and shear strain energy densities on maximum principal strain range plane. Procedures used to determine the normal and shear strain energy densities are also presented. Experimental data taken from the literature are used to validate the capabilities of the improved model, including 4 different metals and 24 different loading paths. The results show that the proposed model gives good predictions for most of these materials and loading paths.

A meshfree method for static and buckling analysis of shear deformable composite laminates considering continuity of interlaminar transverse shearing stresses

A meshfree radial point interpolation method is presented for static and buckling analysis of thick laminated plates, taking into account the continuity of interlaminar transverse shearing stresses and zigzag variation of the displacement field through the plate’s thickness. The kinematics of the deformation field is based on the refined theory of Wang and Shi (2015). The corresponding weak-form for static bending and buckling analyses of plates based on the Wang and Shi’s theory are derived through minimum potential energy principle. The discretized systems of equations for static bending and buckling analyses are derived and the associated numerical integration is performed by the novel CTM quadrature. This integration method can exactly model the problem geometry and thus is very fast and accurate. Several numerical examples are solved to demonstrate the accuracy and efficiency of the plate theory adopted in this paper. Additionally, the examples are also analyzed using the FSDT, TSDT and Shi’s plate theory (2007). Because the four theories considered in this paper use five field variables and they also have some other similarities, the influence of higher order terms of the displacement field, transverse shearing strain energy consistency, and imposition of transverse shearing stress continuity on results is investigated.

Comparing fluid viscous damper placement methods considering total‐building seismic performance

SummaryNonstructural damage has been found to critically influence economic losses and building downtime following earthquakes. Attaining a target level of seismic performance mandates the harmonization of structural and nonstructural performance. Retrofitting buildings with fluid viscous dampers (FVDs) can improve interstorey drifts and floor accelerations, 2 structural parameters that characterize seismic demand on structural and nonstructural systems. The distribution of dampers within a building is a critical decision; however, no conclusive optimal placement method has been identified due to performance variations between storeys and between structural parameters. This paper compares 6 frequently used damper placement methods considering structural and nonstructural repair costs calculated using FEMA P‐58. The scope is limited to linear FVDs, concentric braced frames, and regular structures. Comparisons of the placement methods are based on constraining the added viscous damping coefficient to be the same in each case; this may give different results to methods based on damper cost. No placement method produced optimal results for both interstorey drifts and accelerations. Iterative methods that seek to optimize seismic performance did not achieve that objective. The iterative methods optimize local parameters assuming the performance of each is independent, and optimizing for a single parameter may worsen another parameter that impacts earthquake damage. The storey shear strain energy method and uniform damping generally produced repair costs that are more favorable than, or equal to, the other placement methods. It appears unlikely that large repair cost improvements can be achieved using an “optimal” damper placement method for low‐rise and mid‐rise structures.

A review on the damping properties of fiber reinforced polymer composites

Fiber reinforced polymer composites have great potential for engineering applications. In this work, we have provided a comprehensive review on the damping properties of fiber reinforced polymer composites. This paper has focused on the mechanism and analytical method of damping properties. This work also presents a broad review on several factors which determined the damping, such as matrix, fiber types, fiber architecture, fiber surface modification, and incorporated fillers. We further discussed the role of interfacial region on the improvement of damping, where high shear strain energy is stored at this region. Nanofillers, fiber coating, and interpenetrating polymer networks have high potential for damping treatment. We have concluded this review with some helpful suggestions for the future development of fiber reinforced composites with desired damping properties.

Shear Strain Energy Change Caused by the Interplate Coupling Along the Nankai Trough: An Integration Analysis Using Stress Tensor Inversion and Slip‐Deficit Inversion

AbstractIn the Nankai Trough, southwest Japan, the Philippine Sea plate descends beneath the Eurasian plate. The locking on the plate interface causes stress change in the seismogenic lithosphere of the Eurasian plate. This interplate locking does not always result in stress accumulation but can cause stress release. The present study employs shear strain energy to determine whether the stress is accumulated or released in the seismogenic zone. While most studies employed a shear stress assuming a fault plane, the shear strain energy is more feasible for the stress accumulation/release mapping because the assumption of the fault plane is not required. First, we estimated the directions of the principal stress axes and the stress ratio of the background stress field by analyzing ~8,000 focal mechanisms. In the Chugoku region, the maximum compression axis is in the E‐W direction. We then calculated the stress change due to the slip deficit along the Nankai Trough. The stress change showed that the maximum compression is in the N‐S direction in the Chugoku region. By using both the background stress and the stress fluctuation, we estimated the shear strain energy change caused by the slip deficit. The shear strain energy is decreased due to the interplate locking in the Chugoku region. We also statistically compared the shear strain energy change with the seismicity in southwestern Japan and found that the seismicity is high where the strain energy increases.

Simulation of Shear and Bending Cracking in RC Beam: Material Model and its Application to Impact

This paper presents a simple and reliable non-linear numerical analysis incorporated with fully Lagrangian method namely Smoothed Particle Hydrodynamics (SPH) to predict the impact response of the reinforced concrete (RC) beam under impact loading. The analysis includes the simulation of the effects of high mass low-velocity impact load falling on beam structures. Three basic ideas to present the localized failure of structural elements are: (1) the accurate strength of concrete and steel reinforcement during the short period (dynamic), Dynamic Increase Factor (DIF) has been employed for the effect of strain rate on the compression and tensile strength (2) linear pressure-sensitive yield criteria (Drucker-Prager type) with a new volume dependent Plane-Cap (PC) hardening in the pre-peak regime is assumed for the concrete, meanwhile, shear-strain energy criterion (Von-Mises) is applied to steel reinforcement (3) two kinds of constitutive equation are introduced to simulate the crushing and bending cracking of the beam elements. Then, these numerical analysis results were compared with the experimental test results.

Stacking-fault energy, mechanical twinning and strain hardening of Fe-18Mn-0.6C-(0, 1.5)Al twinning-induced plasticity steels during friction stir welding

The effect of friction stir welding (FSW) on the microstructure, stacking-fault energy (SFE) and strain hardening rate (SHR) of Fe-18Mn-0.6C-(0 and 1.5)Al (wt.%) twinning-induced plasticity steels using three welding speeds (50, 100 and 200 mm min−1) was investigated. The yield strength of the FSWed 0Al and 1.5Al steels improved due to both grain boundary strengthening by grain refinement and dislocation hardening by the introduction of dislocations with an increase in the welding speed. Their SHR with three stages and without the yield drop increased due to the active mechanical twinning and the introduction of dislocations during the FSW when the welding speed was increased. Among the 0Al steels, 0Al-200 steel with a fine grain exhibited more active twinning than the coarse-grained specimen (0Al-50), which is contrast to the 1.5Al steel. Regardless of the specimens, the slight increase in the SFE, which was attributed to both the shear strain energy caused by the introduction of dislocations and the excess free energy by the grain refinement during the FSW, leads to an increase in the critical twinning stress (σtw). Despite the fine grain of the 0Al steel, the origin of its active twinning was the highly increased yield strength relative to σtw, and the promoted dislocation interactions, giving rise to an increase in the number of sites at which twin nucleation occurred.

Thermally induced mechanical analysis of temperature-dependent FG-CNTRC conical shells

A numerical study is performed to investigate the impacts of thermal loading on the vibration and buckling of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) conical shells. Thermo-mechanical properties of constituents are considered to be temperature-dependent. Considering the shear deformation theory, the energy functional is derived, and applying the variational differential quadrature (VDQ) method, the mass and stiffness matrices are obtained. The shear correction factors are accurately calculated by matching the shear strain energy obtained from an exact three-dimensional distribution of the transverse shear stresses and shear strain energy related to the first-order shear deformation theory. Numerical results reveal that considering temperature-dependent material properties plays an important role in predicting the thermally induced vibration of FG-CNTRC conical shells, and neglecting this effect leads to considerable overestimation of the stiffness of the structure.

Modelling multiaxial fatigue with a new combination of critical plane definition and energy-based criterion

A new multiaxial fatigue criterion is proposed that takes into account the influence of material properties and loading conditions on the direction of the critical fatigue plane. Poisson’s effect, normal and shear strain energies, both elastic and plastic, and material hardening can be taken into account in this criterion. Ten different materials subjected to various loading paths with different test-sample geometries are used to validate the capabilities of the proposed approach. The comparison with other commonly used energy-based criteria is also presented. The results show that the proposed criterion provides very good predictions for all the analysed materials and loading conditions (within a factor of two) used in this work. The error in life prediction with the present approach also compares favourably with respect to other criteria available in the literature.