Stress Superposition Research Articles

Stability influence factors analysis and construction of a deep beam anchorage structure in roadway roof

Deep beam anchorage structures based on spatial distribution analysis of the cable prestressed field have been proposed for roadway roof support. Stability and other factors that influence deep beam structures are studied in this paper using mechanical calculations, numerical analysis and field measurements. A mechanical model of deep beam structure subjected to multiple loading is established, including analysis of roof support in the return airway of S1203 working face in the Yuwu coal mine, China. The expression of maximum shear stress in the deep beam structure is deduced according to the stress superposition criterion. It is found that the primary factors affecting deep beam structure stability are deep beam thickness, cable pre-tension and cable spacing. The variation of maximum shear stress distribution and prestressed field diffusion effects according to various factors are analyzed using Matlab® and FLAC3D™ software, and practical support parameters of the S1203 return airway roof are determined. According to the observations of rock pressure, there is no evidence of roof separation, and the maximum values of roof subsidence and convergence of wall rock are 72 and 48 mm, respectively. The results show that the proposed roof support design with a deep beam structure is feasible and achieves effective control of the roadway roof.

Strain Energy-Based Fatigue Life Evaluation of Deck-to-Rib Welded Joints in OSD Considering Combined Effects of Stochastic Traffic Load and Welded Residual Stress

Welded residual stress and stochastic traffic at the deck-to-rib welded joints in the orthotropic steel deck (OSD) of bridges highly affects the fatigue life of bridges. This study presents a strain energy-based method to evaluate the service life of welded joints in the OSD considering the combined effects of traffic load and welded residual stress. Thermomechanical analysis is performed for the welding process of the welded joints using a finite-element model to analyze the distribution of welded residual stress at critical locations of the welded joints. An analysis model is developed to simplify the nonlinear superposition of vehicle-induced stress and welded residual stress. A modified strain energy-based fatigue evaluation approach is presented based on the superposition of stresses. Based on the presented model, a new Wa–Nf curve is proposed to take the effects of welded residual stress into consideration. The presented method is validated against experimental results, and then it is applied to investigate the fatigue life of welded joints in an in-service cable-stayed bridge. The theoretical and inspection results are compared and analyzed. The results show that there is a better coincidence between the predicted fatigue life using the presented approach and the inspected fatigue life in contrast with the conventional approach of neglecting the effects of welded residual stress.

Igneous sills record far-field and near-field stress interactions during volcano construction: Isle of Mull, Scotland

Sill emplacement is typically associated with horizontally mechanically layered host rocks in a near-hydrostatic far-field stress state, where contrasting mechanical properties across the layers promote transitions from dykes, or inclined sheets, to sills. We used detailed field observations from the Loch Scridain Sill Complex (Isle of Mull, UK), and mechanical models to show that layering is not always the dominant control on sill emplacement. The studied sills have consistently shallow dips (1°–25°) and cut vertically bedded and foliated metamorphic basement rocks, and horizontally bedded cover sedimentary rocks and lavas. Horizontal and shallowly-dipping fractures in the host rock were intruded with vertical opening in all cases, whilst steeply-dipping discontinuities within the sequence (i.e. vertical fractures and foliation in the basement, and vertical polygonal joints in the lavas) were not intruded during sill emplacement. Mechanical models of slip tendency, dilation tendency, and fracture susceptibility for local and overall sill geometry data, support a radial horizontal compression during sill emplacement. Our models show that dykes and sills across Mull were emplaced during NW–SE horizontal shortening, related to a far-field tectonic stress state. The dykes generally accommodated phases of NE–SW horizontal tectonic extension, whereas the sills record the superposition of the far-field stress with a near-field stress state, imposed by emplacement of the Mull Central Volcano. We show that through detailed geometric characterisation coupled with mechanical modelling, sills may be used as an indication of fluctuations in the paleostress state.

Boltzmann superposition principle for a time-dependent soft material: assessment under creep flow field

Variety of time-dependent soft materials that undergo evolution of microstructure are known to follow the Boltzmann superposition principle when appropriately transformed from the real to the effective time domain. This behavior is attributed to obliteration of time dependency in the effective time domain by normalizing the real time by the time-dependent relaxation time. This work is aimed at assessing validity of the Boltzmann superposition principle in the effective time domain under application of step changes and ramps in stress for a time-dependent soft glassy material: an aqueous suspension of Laponite, whose rheological properties are known to show strong time and stress dependency. Interestingly, creep experiments started at different aging times and for different constant stresses indeed lead to a comprehensive time–aging time–stress superposition resulting in time and stress dependence of relaxation time and modulus. Subsequently, we analyze compliance response of the material to different kinds of stress step change and ramp combinations. We observe that except few, most of the compliance data plotted in the effective time domain does not overlap on the comprehensive superposition. We analyze this behavior and attribute the observed mismatch to the history dependence of the time evolution of modulus.

The origin of lattice instability in bcc tungsten under triaxial loading

Stability of ideal bcc tungsten crystal under triaxial tensile loading was explored from first principles using an analysis of both elastic and dynamic stability. The triaxial stress state was considered as a superposition of axial and biaxial transverse stresses. The region of attainable stresses which was delimited using the computed tensile stress maxima was marginally reduced by occurrence of soft phonons in the crystal lattice. While, under purely hydrostatic tension, the crystal was predicted stable up to 48 GPa, greater magnitude of a differential stress reduced the value of a mean (hydrostatic) stress associated with first phonon instabilities to about 35 GPa. This value is rather close to that recently determined in experiment. Computed phonon spectra were successfully verified with the help of atomistic models of microscopic lattice deformation.

A systematic methodology for creep master curve construction using the stepped isostress method (SSM): a numerical assessment

Long-term creep of viscoelastic materials is experimentally inferred through accelerating techniques based on the time–temperature superposition principle (TTSP) or on the time–stress superposition principle (TSSP). According to these principles, a given property measured for short times at a higher temperature or higher stress level remains the same as that obtained for longer times at a lower temperature or lower stress level, except that the curves are shifted parallel to the horizontal axis, matching a master curve. These procedures enable the construction of creep master curves with short-term experimental tests. The Stepped Isostress Method (SSM) is an evolution of the classical TSSP method. Higher reduction of the required number of test specimens to obtain the master curve is achieved by the SSM technique, since only one specimen is necessary. The classical approach, using creep tests, demands at least one specimen per each stress level to produce a set of creep curves upon which TSSP is applied to obtain the master curve. This work proposes an analytical method to process the SSM raw data. The method is validated using numerical simulations to reproduce the SSM tests based on two different viscoelastic models. One model represents the viscoelastic behavior of a graphite/epoxy laminate and the other represents an adhesive based on epoxy resin.

Theoretical and Numerical Investigation on Rock Fragmentation Under High-Pressure Water-Jet Impact

According to the load characteristics of high-speed water-jet impacting on rock, the hammer pressure, which is a function of time, is regarded as the dynamic load acting on the rock. The theoretical model of rock fragmentation via water-jet impact was set up, and the rock stress and displacement were obtained based on the theory of shock waves. Considering the rock failure criterion and the attenuation characteristic of the stress wave, the scopes of the rock crushing zone and damage zone were established. The numerical model of rock fragmentation via water-jet impact was developed based on the modified maximum principal stress criterion, and the formation of the rock crushing zone, damage zone, radial crack and spall crack was well simulated. The theoretical scopes of the crushing zone and damage zone were slightly smaller than those of the numerical method, because the stress wave reflection and superposition were ignored in the theoretical model. The formation mechanism of the crushing zone, radial crack and spall crack was investigated by analysing the element stress changes as a function of time in different positions.

The sling anchorage: Approach to anchor the full load bearing capacity of pin-loaded straps

Tension members are a promising application for carbon fibre reinforced polymers (CFRP) in civil engineering. Anchoring CFRP tension members is a significant challenge due to their relatively low strength and low Young’s modulus in the transverse direction. The laminated loop anchorages of pin-loaded straps are strong and lightweight force locking connections. However, the load bearing capacity of those anchorages is limited to about 70% of the tension members’ breaking load due to the superposition of tension and bending stress at the pin. In this paper, an alternative design for pin-loaded straps (the sling anchorage) is proposed that increases the load bearing capacity up to 100%. This increase is predicted using a theoretical approach from the literature. Numerical and experimental results are presented to characterize the structural behaviour of the sling anchorage. The experimental results show that the sling anchorage can achieve the predicted load bearing capacity. Furthermore, a manufacturing method that allows forming the sling anchorage at the ends of parallel CFRP tapes (or pultruded profiles) is also introduced.

Magnetically Controlled Saturable Reactor Core Vibration Under Practical Working Conditions

In order to seek new vibration reduction method for magnetically controlled saturable reactors (MCSRs), this paper studies the stress characteristic which is the inherent reason of vibration and noise. Under the practical working condition, dc and ac excitations make iron cores work in a magnetic saturation state. Meanwhile, the stress in reactor cores always exists and influences on magnetic properties of the core material. Because the core material shows different magnetization and magnetostrictive properties under dc bias and stress, a database of magnetization and magnetostrictive curves of silicon steel under different tensile stresses with different dc bias excitations is tested. Based on the measured constitutive relations, an electromagneto-mechanical two-way coupled numerical model for MCSRs is presented. Vibrations considering magnetostrictive effect, electromagnetic force effect, and the combination of them are calculated to compare the influence of the two forces on MCSR vibration. From the computation results, it can be seen that the total vibration stress is not a simple superposition of electromagnetic stress and magnetostrictive stress. Finally, vibration stress of an MCSR prototype under working conditions is tested to prove the validity of the proposed model.

Biaxial tension-torsion fatigue behavior of gradient nano-grained pure titanium fabricated by surface nanocrystallization

A gradient nanostructured surface layer was fabricated in the commercial-purity titanium (Ti) thin-wall tubular sample using the modified surface nanocrystallization (SNC) technique. Biaxial tension-torsion fatigue behavior of the SNC Ti was investigated. The SNC Ti shows significant longer biaxial fatigue lives than the coarse grained Ti (CG Ti) at the same cyclic equivalent stress amplitude. Both CG and SNC Ti display hardening during cyclic deformation, and the hardening level in the SNC Ti is larger than that of the CG one. Microstructural analysis reveals that the SNC Ti shows hierarchical deformation mechanisms in different areas across the wall-thickness of tubular samples during biaxial fatigue. In the nano/ultrafine grain region, the stress-driven nanograin growth is the primary deformation mechanism. In the deformed grain region, the interaction between lamella structure and dislocations is observed. In the coarse grain region, prismatic slip is main deformation mode. The initiation of fatigue cracks is restricted in the SNC Ti since the stress concentration is relieved through stress-driven nanograin growth during cyclic deformation. The initiation mechanism of fatigue cracks transforms from slip band and grain boundary cracking in the CG Ti to the shear band cracking in the SNC Ti. Furthermore, since the superposition of residual compressive stress with the exterior applied stress in the SNC Ti, both maximum shear stress and maximum normal stress are decreased. Consequently, the equivalent driving forces for crack initiation and propagation in the SNC Ti are smaller than those in the CG Ti. The higher resistance to fatigue crack initiation and the lower equivalent driving force for fatigue crack initiation and propagation contribute to the enhancement of fatigue properties in the SNC Ti.

Ultrafast Displacement Actuation of Piezoelectric Stacks With Time-Sequence

Driving a piezoelectric stack with fast response and high output force is critical for its application. A novel ultrafast time-sequence driving method for piezoelectric stacks that could be used in fuel injectors is described and demonstrated. This technique is shown capable of reducing the response time of a piezoelectric stack by considering the stress wave propagating in the stack. Stress wave propagation in a piezoelectric stack is analyzed, and a time-sequence circuit is specially designed to generate driving signals. A piezoelectric stack with 14 layers is fabricated and tested with traditional and time-sequence driving methods. Experimental results show that a linear superposition of stress generated by each piezoelectric layer is obtained and the response speed of the piezoelectric stack is more than doubled. Besides, the generated instantaneous force is also improved considerably.

Study on influence of additive and host ions on deformation characteristics of alkali halide crystals by strain‐rate cycling tests during the Blaha effect

Strain‐rate cycling tests associated with ultrasonic oscillation were carried out between the strain rates () of 1.1×10−5 s−1 and 5.6×10−5 s−1 for NaBr:Li+ or K+ single crystals from 77 K up to the room temperature. Superposition of oscillatory stress during plastic deformation causes a stress drop (Δτ). By using the stress change (Δτ') due to the strain‐rate cycling keeping the stress amplitude constant, Δτ'/Δln was given as a measurement of the strain‐rate sensitivity (λ) of flow stress. The relative curve of and λ has a stair‐like shape for the two kinds of crystals at low temperature (T). That is to say, the curve has two bending points and two plateau regions and λ between the two bending points decreases gradually with increasing . The activation energy (G0) etc. concerned with the break‐away of a dislocation from the isotropic strain around additive cation could be obtained on the basis of three relative curves (τp vs. T, λp vs. T, and τp vs. V) fitting the Cottrell‐Bilby relation to the experimental results. τp is Δτ value of first bending point at low stress decrement and λp is the difference between λ at first plateau place and at second one on the curve of vs. λ. V is the activation volume obtained from λp. As a result, it was found that Li+ ions are slightly weaker than K+ ones as weak obstacles to dislocation motion in the crystals. Furthermore, the additive Li+ or K+ ions act as still weaker obstacles to dislocation motion in NaBr host crystal as against NaCl because of a slight reduction in G0.

Application of time–stress superposition to viscoelastic behavior of polyamide 6,6 fiber and its “true” elastic modulus

ABSTRACTThe viscoelastic behavior of semi‐crystalline polyamide 6,6 fiber is exploited in viscoelastically prestressed polymeric matrix composites. To understand better the underlying prestress mechanisms, strain–time performance of the fiber material is investigated in this work, under high creep stress values (330–665 MPa). A latch‐based Weibull model enables prediction of the “true” elastic modulus through instantaneous deformation from the creep‐recovery data, giving 4.6 ± 0.4 GPa. The fiber shows approximate linear viscoelastic characteristics, so that the time–stress superposition principle (TSSP) can be implemented, with a linear relationship between the stress shift factor and applied stress. The resulting master creep curve enables creep behavior at 330 MPa to be predicted over a large timescale, thus creep at 590 MPa for 24 h would be equivalent to a 330 MPa creep stress for ∼5200 years. Similarly, the TSSP is applied to the resulting recovery data, to obtain a master recovery curve. This is equivalent to load removal in the master creep curve, in which the yarns would have been subjected to 330 MPa creep stress for ∼4.56 × 107 h. Since our work involves high stress values, the findings may be of interest to those involved with long‐term load‐bearing applications using polyamide materials. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017, 134, 44971.

Lithospheric stress in Mongolia, from earthquake source data

Lithospheric stress in Mongolia has been studied using mechanisms of 84 MLH ≥ 4 earthquakes that occurred in the 20th century and instrumental seismic moments of 17,375 MLH ≥ 2.5 events recorded between 1970 and 2000. The MLH ≥ 3.5 earthquakes mostly have strike-slip mechanisms in southern and central Mongolia, with frequent reverse-slip motions in the west and normal slip in the north, especially, in the area of Lake Hovsgol. The principal stresses are, respectively, SH>Sv>Sh in the center and in the south; high horizontal compression with SH>Sh>Sv in the west; and a heterogeneous stress pattern with Sv>SH>Sh in the north. According to seismic moments of MLH = 2.5 events, oblique slip generally predominates over the territory, at Sv≈SH>>Sh, while frequent strike slip motions in the west record high horizontal compression (SH>Sv>Sh). Earthquake mechanisms show the principal horizontal compression SH to be directed W–E in the east, NE–SW in the central and Gobi-Altay regions, and approximately N–S in the west of Mongolia. The patterns of principal lithospheric stresses in the territory of Mongolia have undergone three events of dramatic change for a few recent decades, and these events were synchronous with three similar events in the Baikal rift system (BRS): in the latest 1960s, latest 1970s to earliest 1980s, and in the latest 1980s to earliest 1990s. The seismicity of Mongolia has been controlled by superposition of variable stresses associated with rifting activity pulses in the neighbor BRS on the background of quasi-stationary super-regional compression.

Aging life evaluation of a new carbon fiber composite core wire

The carbon fiber composite core wire is the key component for new overhead transmission lines in the power industry. As the primary load-bearing member, the composite mandrel will produce long-term creep because of the tensile during operation. Therefore, designers need to understand the long-term deformation behaviour of the composite mandrel to assess its durability. To this end, an accelerated creep test on the composite core rod under different temperatures and stresses has been conducted in the current study. According to the time- temperature- stress superposition principle, the shift factors are calculated, and the creep under normal working condition is predicted. Results show that the carbon fiber composite core wire can satisfy the design requirements under normal working condition.

Forming-induced damage and its effects on product properties

Damage is caused in the microstructure of metals during forming. Damage is not a failure, but affects the mechanical properties of the component under service loads. This paper explores experimentally the effect of metal forming process parameters on the evolution of damage and the resulting product properties. As a representative for bulk forming processes, cold forging is investigated. It is shown that an increase of the extrusion ratio leads to lower damage and increased fatigue strength. Air bending, as a sheet forming process, is analysed, exhibiting that damage can be influenced by process design such as the superposition of stresses.

Compression testing of martensitic stainless steel with superimposed ultrasonic vibration

Abstract The expanding use of materials with high strength in cold forging and the associated force increases as well as the limited formability present a major challenge for conventional process technology. One method to respond to this challenge is the use of high frequently oscillating forming tools which lead to a decrease of the required forces. Previous research on this topic has focused on fairly soft materials, such as aluminum. Materials with higher strength have only been analyzed to a very limited extent. This study addresses the ultrasonic-assisted compression testing of high strength martensitic stainless steel with 20 kHz oscillation frequency aiming at the identification of relevant process parameters and the partial separation of occurring effects. Experimental investigations are carried out to analyze the effect of ultrasonic-assistance during compression testing with varying oscillation duration and amplitude on the maximum forming force and on specimen heating. To isolate the proportional force reduction due to material heating from other oscillation induced causes, a comparison with conventional warm compression tests is performed. Finally, a simplified numerical simulation which is able to model the ultrasonic-assisted compression test is proposed. The experimental results reveal a strong influence of the oscillation amplitude on the reduction of maximum forces and on specimen heating. The oscillation duration presents a minor influence on the maximum forces, but strongly affects the heat generation. The developed simulation model is in good accordance with experimental force displacement curves and allows the separation between stress superposition and other ultrasonic-induced effects.

The reciprocal effects of bending and torsion on springback during 3D bending of profiles

Abstract Profiles with circular cross-sections can be geometrically described by the shape of the bending line. To achieve 3D bending lines with kinematic bending processes, a continuous change of the bending plane is needed, resulting in bending force vectors that change in direction accordingly. These force vectors generate a bending moment in the forming zone and, thus, longitudinal tensile and compressive stresses. For profiles with non-circular cross-sections, the orientation of the cross-section along the bending line needs to be additionally controlled. This can be achieved by applying a specific torque to the bending process and, thus, introducing desired shear stresses into the forming zone. Up until now, this fundamental aspect of 3D profile bending has not been regarded in a coherent fashion. To take into account the reciprocal effects of the stresses applied to the forming zone and their effect on the bending moment and, thus, on springback, a comprehensive analytical process model was set up. The model is validated by experimental investigations performed using the TSS profile bending machine and comprehensive numerical investigations. Analyses were performed during plane bending as well as bending superposed with torsion. The investigations show that the applied bending force and torque not only result in stress superposition but actually also affect the development of shear strains over the cross-section of the profile. Similar to the longitudinal strains, the shear strains decrease linearly from the intrados and extrados of the profile to the neutral axis. Considering this newly observed behavior in the analytical process model, the bending moment prediction is in accordance with the experimental and numerical results.

Impact effect of superimposed ultrasonic vibration on material characteristics in compression tests

Abstract Conventional ultrasonic-assisted forming in macro scale has been studied widely for decades. However, ultrasonic dynamic impact effect, which only occurs in micro-scale, has never been studied thoroughly. The purpose of this study is to investigate and identify the influencing parameters of amplitude and vibration time for the ultrasonic-induced stress reduction considering dynamic impact effect. As the first step for the purpose, commercially pure aluminum 1100 with specimen size of 2 mm in diameter and height were selected for ultrasonic-assisted compression tests with varying amplitude and press speed. Ultrasonic-induced stress reduction was evaluated and the contour shape of deformed specimens was compared to obtain the effect of ultrasonic vibration on material deformation. The results showed that, ultrasonic dynamic impact effect was the dominating mechanism for stress reduction in compression condition, the stress reduction which caused was nearly 5 times of the sum by stress superposition and acoustic softening. The ratio of amplitude to specimen height is identified as an influencing index for occurrence of ultrasonic dynamic impact effect, for which the critical value equals to half of yield strain. The findings showed promising prospect of ultrasonic vibration in micro-forming, which helped to provide a basis to understand the underlying mechanism of ultrasonic-assisted micro-forming and design the process in next step.

Competing Indentation Deformation Mechanisms in Glass Using Different Strengthening Methods

Chemical strengthening via ion exchange, thermal tempering, and lamination are proven techniques for strengthening of oxide glasses. For each of these techniques, the strengthening mechanism is conventionally ascribed to the linear superposition of the compressive stress profile on the glass surface. However, in this work we use molecular dynamics simulations to reveal the underlying indentation deformation mechanism beyond the simple linear superposition of compressive and indentation stresses. In particular, the plastic zone can be dramatically different from the commonly assumed hemispherical shape, which leads to a completely different stress field and resulting crack system. We show that the indentation-induced fracture is controlled by two competing mechanisms: the compressive stress itself and a potential reduction in free volume that can increase the driving force for crack formation. Chemical strengthening via ion exchange tends to escalate the competition between these two effects, while thermal tempering tends to reduce it. Lamination of glasses with differential thermal expansion falls in between. The crack system also depends on the indenter geometry and the loading stage, i.e., loading vs. after unloading. It is observed that combining thermal tempering or high free volume content with ion exchange or lamination can impart a relatively high compressive stress and reduce the driving force for crack formation. Therefore, such a combined approach might offer the best overall crack resistance for oxide glasses.