Pure Shear Mode Research Articles

Cohesive failure analysis of carbon-fiber composite patch repair in perforated steel tubular elements

The use of composite materials to repair corroded steel structural components has expanded in the offshore oil and gas sector. The effective use of composites requires a meticulous process for choosing appropriate constituent elements. In this regard, numerical modeling is an efficient tool to better understand the impact of associated variables and enables the identification of failure causes and simulation of failure propagation. This study aims to assess the mechanical behavior of the adhesive layer at the steel - composite material interface in the repair of perforated tubular structures under bending, compression, and bending-compression. A numerical model is developed simplifying the examination and characterization of the cohesive failure mechanisms and modes occurring between the laminate patch repair and the perforated steel tubular element. The stress distribution and cohesive failure at the interface are then thoroughly investigated. The impacts of the inclusion of fillets at the patch repair ends to smoothen the transition between the composite material and the tube and the repair length are also evaluated. A Python subroutine is developed to identify the failure mode mechanisms to characterize the adhesive areas subjected to peel, shear, or mixed modes. Results suggest that pure shear mode is predominant in most of the repair locations across the three types of loading. For bending loads, the cohesive failure close to the cutout shows prominent shear mode. In the other loading conditions, the adhesive nearly fails in the vicinity of the cutouts (i.e., damage values are close to 1) in a predominant near pure shear failure mechanism. The use of fillets displaces the failure location for bending load, hence increasing the failure load level. Repairs were more extensive under Bending Moment load conditions compared to other load types. The mode ratio analysis and methodology presented in this work offer valuable tools for understanding the causes of failure modes.

Notch strength evaluation for highly ductile Al/Cu bi-metal fabricated by the roll-bonding technique under pure mode I and pure mode II loading conditions

In this work, the aluminum alloy AA1050 and copper sheets are cladded together using the roll-bonding technique to make rectangular bi-metallic joints. To examine the notch strength of this bi-metal under quasi-static loading, central slits with two U-shaped ends are introduced into the bi-metal. The slit orientation angle is adopted such that for horizontal slit, the notched rectangular specimen experiences pure mode I loading. However, when the slit orientation angle changes to about 67 degrees, which is obtained by the finite element (FE) analysis, the U-ends of the slit are subjected to pure mode II loading. Considering three different notch tip radii, two loading conditions, and three replicates for each test configuration, totally 18 U-notched specimens are produced and tested with the goal to measure the notch strength of bi-metal experimentally. According to the experimental observations, the bi-metal joint is perfect such that crack initiates from the notch in the whole thickness, proposing that the whole bi-metal joint can be considered as a single bulk material. Based on these observations and thanks to the virtual isotropic material concept (VIMC), the AA1050/Cu bi-metal is firstly equated with a virtual bulk material having homogeneous and isotropic behavior. Secondly, due to highly ductile behavior of the bi-metal joint proven by the associated tensile stress–strain curve, the fictitious material concept (FMC) is used to equate the virtual isotropic material obtained from the previous step having elastoplastic behavior with a fictitious material having perfectly linear elastic behavior. Finally, the VIMC and FMC are linked to the U-notch maximum tangential stress (UMTS), U-notch mean stress (UMS), and U-notch strain energy density (USED) criteria to predict the notch strengths of the bi-metal joint experimentally measured. With always higher than 92% accuracy for all VIMC-FMC-UMTS, VIMC-FMC-UMS, and VIMC-FMC-USED combined criteria, it is shown that the two-level strategy of material simplification, i.e., VIMC-FMC, is quite successful to be combined with different brittle fracture criteria for predicting the notch strength of AA1050-Cu bimetals under both pure tensile and pure in-plane shear modes of loading.

Tunable pure shear deformation of voltage/charge loaded dielectric elastomers

The pure shear mode can achieve a large and stable deformation in the actuation of dielectric elastomers (DEs). In this paper, based on our previously designed deformation controller, we propose the method of tuning two inplane stresses and applied voltage/charge to realize precise pure shear deformation, by deducing the governing equations of voltage- and charge-loaded DEs. The evolution of electromechanical stabilities of voltage- and charge-loaded DEs under pure shear deformation mode is considered. The maximum stable electromechanical deformation related to electromechanical failures is simultaneously calculated. It is found that the stable deformation and parameter variation tendency have different dependency for the loading modes of DEs. The critical conditions of occurrence of possible electromechanical failures are also clarified. This research can be utilized to beforehand select the tension stresses and applied voltage/charge to strengthen the electromechanical stability of DEs in pure shear deformation mode.

Shear vibration modes of granular structures: Continuous and discrete approaches

AbstractThis work is dedicated to the study of shear vibration modes of one‐dimensional granular microstructured beams using a discrete Cosserat model. The dynamic response of the one‐dimensional granular beam (discrete beam) is investigated for various boundary conditions, through the analytical resolution of an exact discrete eigenvalue problem. For an infinite number of grains, the dynamic behavior of the discrete problem converges towards a Bresse–Timoshenko continuum beam model. First, the effective modeling parameters, the constitutive equations and the governing equations of motion are derived in a difference form. For simply supported granular beams, the appearance of pure shear modes of vibration is highlighted (vibration modes without deflection), a phenomenon which is already known in the free vibration of a continuous Bresse–Timoshenko beam problem. The eigenfrequencies of these pure shear modes for the discrete granular beam coincide with the critical frequencies of the discrete system. These pure shear modes may appear for granular beams composed of few grains, which give a physical support of a phenomenon well studied in the literature from a continuum beam model. The eigenfrequencies of the discrete granular beam are also calculated for various boundary conditions, including clamped, hinge and free end boundary conditions. Based on the discrete element method (DEM), several numerical simulations of dynamic tests in some representative examples have been performed. The responses of the numerical approach are accurately compared against the exact results of the analytical solutions based on the difference eigenvalue problem, which illustrates the relevance of the proposed approach.

Experimental and statistical exploring for mixed-mode (I&II) fracture behavior of cement emulsified asphalt mortar under freeze–thaw cycles and aging condition

This study has been investigated the effect of freeze–thaw cycles and aging condition on the pure mode I, pure mode II and mixed-mode I/II fracture resistance of Cement Emulsified Asphalt Mortar (CEAM). The experiments were conducted on SCB specimens designed with 16 randomized mix designs with different cement contents (C), asphalt-to-cement ratios (A/C), and water-to-cement ratios (W/C) using the d-optimal response surface methodology. The specimens were divided into three groups: control specimens (n = 144), aged specimens (n = 144), and specimens subjected to 1, 3, 5, and 10 freeze–thaw cycles (n = 576). The experiments were performed in three modes of loading: pure tensile (I), pure shear (II), and mixed-mode tensile-shear (I/II). To assess the impact of freeze–thaw and aging damage on fracture properties, the Fracture Energy Ratio (FER) was defined as the ratio of fracture energy of the damaged/conditioned specimen to that of the corresponding control specimen. Then, a number of statistical models were developed for the relationship between FER and mix design variables (A/C, W/C, and C). The results showed that the application of freeze–thaw cycles reduced the fracture energy of CEAM in all three modes. The independent variable with the greatest impact on fracture energy changes was A/C for the pure tensile mode, and C for the pure shear mode and the mixed-mode tensile-shear. The initial freeze–thaw cycles were found to have a greater impact on fracture energy than later cycles. Also, freeze–thaw cycles are more detrimental in reducing mode II fracture energy than mode I and mixed-mode I/II fracture energies and therefore have a more damaging impact on the pure shear fracture properties of CEAM. Aging also reduced the fracture energy of CEAM in all three modes; an effect that was most greatly influenced by the amount of asphalt in the mortar composition. Aging had a greater impact on mode I fracture energy than mode II and mixed-mode I/II fracture energies.

Mixed mode-I/II fatigue performance of Cement Emulsified Asphalt Mortar: Experimental and statistical analysis at intermediate temperature

This study has investigated fatigue life of Cement Emulsified Asphalt Mortar (CEAM) under mixed-mode I/II loadings at the intermediate temperature. For this investigation, SCB specimens of 16 randomized mixture designs with different cement contents (C), asphalt-to-cement ratios (A/C), and water-to-cement ratios (W/C) were prepared and subjected to the cyclic mixed tensile-shear loading with Me = 0, 0.5, 1.0 at three frequencies of 2, 4 and 8 Hz. The results were analyzed using the d-optimal response surface method and revealed that for all three loading modes, the fatigue life increased with increasing C and A/C. The CEAM also showed a longer fatigue life in the pure shear mode than in the pure tensile mode. The difference between the fatigue life of mode I and II was found to be increasing with the increase in cement content and loading frequency. Increasing the loading frequency increased the fatigue life of the mortar in all three modes.

Development of a new magnetorheological impact damper with low velocity sensitivity

The velocity sensitive characteristic of the conventional linear magnetorheological (MR) damper is undesirable in the application of impact protection. It will induce large damping forces when the damper suffers high velocity impacts, whilst comprising the energy dissipation efficiency of the damper and posing a serious threat to occupants and mechanical structures. This work reports a new MR impact damper (NMRID) with low velocity sensitivity. Unlike the conventional MR impact damper (CMRID) in which MR fluids (MRFs) flow from one chamber to the other through a small annular gap between the piston and cylinder, the NMRID has a whole annular gap between the shaft and cylinder that is filled with MRFs, and the MRFs work in a pure shear mode without any liquid flow. In this work, a NMRID and a CMRID were prototyped. The velocity sensitivities of these two impact dampers were compared via numerical analysis and experimental impact tests. The analysis and test results indicate that NMRID possesses a much lower velocity sensitivity than the CMRID; the dynamic range of the NMRID decreases less than CMRID with the increase of nominal impact velocity. Then, to demonstrate the controllability of NMRID, impact tests with a bang–bang control were implemented, and the peak force of NMRID was successfully controlled around a target force under different levels of nominal impact velocity. This research proves that the designed NMRID is less sensitive to velocity than the CMRID and the NMRID has good controllability, demonstrating that the NMRID can serve as a better candidate than CMRID in applications with high impact velocity.

Numerical study on liquefaction characteristics of granular materials under Rayleigh-wave strain conditions using 3D DEM

In liquefaction analyses, liquefaction is conventionally assumed to originate from the vertical propagation of shear waves. However, some field and theoretical evidence has demonstrated that the risk of liquefaction may be induced or increased by surface waves. In this study, the liquefaction characteristics of K0-consolidated granular materials under Rayleigh-wave strain conditions, ideal deformation conditions under the assumption of constant volume, were investigated by the three-dimensional discrete element method (3D DEM). The results indicate that Rayleigh-wave strain conditions combine pure and simple shear modes. As the ratio of the shear strain amplitude to the normal strain amplitude (RSN) increases from 1 to +∞, granular materials tend to have a slower liquefaction rate and higher liquefaction resistance; however, the difference in the undrained responses is negligible when the RSN is less than 1. The distribution of the magnitude and orientation of the contact forces also varies with the RSN, while it is similar when the RSN is less than 1. The degradation of the skeleton structure and the evolution of the structural anisotropy accelerate the liquefaction of granular materials. Moreover, in situations with the same accumulated equivalent strain per cycle, the Rayleigh-wave strain condition with a low RSN value will make granular materials more vulnerable to liquefaction compared with Love- and SH-wave strain conditions.

Physics-informed machine learning model for computational fracture of quasi-brittle materials without labelled data

Only a few studies have focused on the simulation of the crack propagation of quasi-brittle materials under complex loading inspired by physical-informed neural networks (PINN). Guided by the energy minimization principle rather than labelled data, we reconstruct the solution of displacement field after damage to predict crack propagation using PINN which maintains the thermodynamics consistency inherited from our proposed variable four-parameter damage model. Additionally, the framework of incremental pattern performs relatively efficiently with transfer learning. Consequently, a novel method for better convergence based on domain decomposition theory is proposed to identify complex boundaries. Based on gradient pathology, we develop a finite basis algorithm to solve the ill-condition problem. Whether under uniaxial tension, pure shear or mixed mode loading, the prediction results of displacement field fit well with simulations in the literature. Our research is meaningful for improving the generalization of neural networks and accelerating the optimization process which are necessary for further engineering applications.

Numerical modeling of metamorphic core complex formation: Implications for the destruction of the North China Craton

Widespread magmatism, metamorphic core complexes (MCCs), and significant lithospheric thinning occurred during the Mesozoic in the North China Craton (NCC). It has been suggested that the coeval exhumation of MCCs with uniform northwest-southeast shear senses and magmatism probably resulted from a decratonization event during the retreat of the paleo-Pacific Plate. Here we used two-dimensional finite element thermomechanical numerical models to investigate critical parameters controlling the formation of MCCs under far-field extensional stress. We observed three end-member deformation modes: the MCC mode, the symmetric-dome mode, and the pure-shear mode. The MCC mode requires a Moho temperature of ≥700 °C and an extensional strain rate of ≥5 × 10⁻¹⁶ s⁻¹, implying that the lithosphere had already thinned when the MCC was formed in the Mesozoic. Considering that the widespread MCCs have the same northwest-southeast extension direction in the NCC, we suggest that the MCCs are surface expressions of both large-scale extension and craton destruction and that rollback of the paleo-Pacific slab might be the common driving force.

3-Dimentional Elucidation of Fatigue Characteristics and Fracture Morphologies in Spot Welding Joints of High Strength Steel

In order to investigate the three-dimensional fatigue properties of resistance spot welded joints made of high strength steel, this study was carried out observed three-dimensional fatigue cracks and calculated stress intensity factors using fem analysis. In addition, this study was conducted under shear mode and pure shear mode to investigate the influence of loading mode during fatigue testing. As a result, it was found that a new crack growth behavior branched in the welding circumferential and width direction under the low loading force range. However, all the cracks leading to final fracture were of the same type, and it was confirmed that the fatigue strength was not affected by a new crack growth behavior. Moreover, the results of observed initial fatigue crack growth angles and the calculated stress intensity factor, KIθ, were in close agreement, which proved that the fatigue crack growth behavior was strongly influenced by the fracture mechanics.

Realizing pure shear mode of dielectric elastomers by tuning biaxial prestress of a deformation controller

In this article, we propose a method to realize the pure shear deformation mode of dielectric elastomer (DE) membranes by tuning two in-plane prestresses. With utilization of carbon grease electrodes, VHB 4905 membranes are prestretched and attached into a retractable device, forming a pure-shear deformation controller. Experimental results demonstrate that, accurate pure shear deformation mode of DEs can be realized by tuning the mechanical loads in the two directions of the deformation controller. Furthermore, large deformation in the direction of free state can be achieved without electromechanical instabilities. The designed deformation controller accurately realizes the specific pure shear deformation mode of DEs and can be utilized to help design the practical soft actuators.

Temperature-Dependent Viscoelastic Energy Dissipation and Fatigue Crack Growth in Filled Silicone Elastomers

There has always been a need to investigate the mechanical properties and fracture behaviors of materials that are widely used commercially, such as filled silicone rubbers. In this work, a thorough study was performed to evaluate the temperature dependencies of viscoelastic energy dissipation and fatigue crack propagation. Small strain viscoelastic behavior was examined by using dynamic mechanical analysis (DMA), and larger strain viscoelastic dissipation was quantified by defining an effective viscoelastic phase angle from large-amplitude cyclic deformation. Pure shear mode I fatigue tests were performed for quantification of material toughness and crack propagation resistance. In addition, natural rubber with different filler levels was tested to provide a direct comparison between two important classes of filled rubber elastomers. Major differences were identified for the two elastomers. However, for both types of elastomers, a common power law relationship with an exponent of 1.5 describes the dependence of the fatigue crack growth per cycle on a normalized driving force obtained from the stored elastic energy. We found that the silicone rubber deviated from the 1.5 exponent power law relation at elevated temperature, and its prefactor in this power law was correlated to the crack morphology, with rough cracks providing a higher fatigue resistance than smooth cracks.

A macro-modelling approach for arches strengthened with externally bonded inorganic matrix composites

The use of externally bonded inorganic matrix composites is becoming a common technique for strengthening arches and vaults to improve the load-carrying capacity with respect to both static and seismic loads. Experimental evidence has shown a complex behaviour where failure may occur within the reinforcement matrix, with a strong coupling between pure opening mode (mode I) and shear mode (mode II), as a consequence of the curvature of the substrate.Aiming at providing a tool for simulating the structural behavior of masonry arches reinforced with inorganic matrix composites, a discrete macro-modeling approach is proposed in which the reinforcement is described by means of piecewise rigid plates, which interact with the masonry through zero-thickness nonlinear interfaces. A refined bond constitutive law, specifically conceived to account for both the cohesive and the frictional contributions, as well as the coupling between mode I and mode II, in terms of strength and softening behavior, is proposed and implemented in a macro-elements model. The proposed model is then validated through comparison with analytical predictions and experimental direct shear tests performed with straight and curved substrates. Eventually, the model is used to reproduce the behaviour of a barrel vault strengthened with steel reinforced grout and tested up to failure.

Compressive Behavior of (Cu0.47Zr0.45Al0.08)98Dy2 Bulk Metallic Glass at Different Strain Rates.

The mechanical properties of (Cu0.47Zr0.45Al0.08)98Dy2 bulk metallic glass (BMG) were characterized under various strain rates by quasi-static and dynamic compressive tests. In the quasi-static compressive tests, the yield stress of (Cu0.47Zr0.45Al0.08)98Dy2 BMG increased from 1234 MPa to 1844 MPa when the strain rate was increased from 0.001 s−1 to 0.01 s−1, and the yield stress decreased to 1430 MPa at the strain rate of 0.1 s−1. In the dynamic compressive tests, when the strain rate increased from 1550 s−1 to 2990 s−1, the yield stress of (Cu0.47Zr0.45Al0.08)98Dy2 BMG first decreased from 1508 MPa to 1404 MPa, and then increased to 1593 MPa. The fracture behaviors of (Cu0.47Zr0.45Al0.08)98Dy2 BMG were studied by using scanning electron microscopy to examine the fracture surface. Fracture occurred in the pure shear mode with strain rates below 2100 s−1, whereas shear fracture and normal fracture occurred simultaneously under strain rates of 2650 s−1 and 2990 s−1.

Finite element analysis of plastic deformation in shear punch test

Strain level and mode of deformation in shear punch testing (SPT) was investigated by finite element method (FEM). The value of equivalent plastic strain was related to the punch displacement (d), punch-die clearance (W), and sample thickness (t) by the relationship of ε∝d/tW. Based on the numerical simulation, it was inferred that the deformation mode depends on the clearance and thickness. It was shown that W/t = 0.1 corresponds to the pure shear mode for AISI 304L austenitic stainless steel, for which the axial components of the plastic strain tend to zero. These findings were found to be consistent with experimental observations and can be utilized in future studies on the mechanical properties and microstructure evolution of materials.

Fracture assessment of pipeline girth weld at low temperature

The results of long-distance oil and gas pipeline failure analysis are important to the industry in order to maintain the reliability and safety of them. Seam welding in these pipes is done with good accuracy at place of work, while girth welding is carried out in the installation site and usually causes the main failure problem. Therefore, the most vulnerable and crucial part of these pipes is the girth welding. Investigating the fracture behavior of girth weld in high-pressure gas pipeline systems at low temperatures is important because these products are hazardous and may lead to explosion, leading to economic losses and environmental pollution. In the present study, the fracture behavior of girth-welded API 5L X65 natural gas transportation pipes was experimentally investigated at low temperatures. The fracture parameters were obtained using Arcan fixture in which all of the in-plane modes including pure tensile mode to pure shear mode can be created by altering the loading angle from 0° to 90°. Finite element analysis was also conducted by ABAQUS finite element software in order to determine geometrical coefficients which are required in calculating the fracture toughness. Results revealed that by decreasing the temperature and increasing the mode II loading contribution, the fracture toughness values were also decreased.

Low temperature fracture resistance of cement emulsified asphalt mortar under mixed mode I/III loading

Having asphalt in Cement Emulsified Asphalt Mortar (CEAM), this composition has higher toughness and ductility but also higher thermal sensitivity than conventional cement mortar. This study was aimed at investigating the fracture behavior of CEAM under out-of-plane shear and tensile loadings (Mode I, I/III, III) at low temperature. This investigation was performed by testing Edge Notched Disc Bending (ENDB) specimens with different asphalt-to-cement and water-to-cement ratios at three temperatures. Scanning Electron Microscopy technique (SEM was also employed to evaluate the effect of asphalt-to-cement and water-to-cement ratios on the structure of CEAMs. The findings revealed that for CEAM, the fracture toughness attains its highest value at pure tensile mode I, decreases as the share of out-of-plane shear in the mixed-mode I/III loading increases, and reaches its lowest value in the pure out-of-plane shear mode III. Furthermore, a multiple regression model was extracted for the relationship between each critical stress intensity factor (KC) and asphalt-to-cement ratio (A/C), water-to-cement (W/C), and temperature (T). The analyses showed -at the 95% confidence level- that A/C have a significant impact on KC in all examined modes and also the fracture toughness of CEAM decreases with increasing A/C. Changes in W/C also had a significant impact on the pure shear mode and mixed tensile-shear mode (I/III) stress intensity factors. Temperature changes in the studied range only affected the pure tensile mode stress intensity factor.

Structural response of metal sheets under combined shear and tension

The structural response of metal sheets under various in-plane loads are investigated in this article using a combined experimental and numerical approach. For this purpose, four different specimen shapes, made from 2 mm thin sheets of aluminum (AL1100) and mild steel (IS 1570), are tested at different loading angles, e.g., pure shear (0°), pure tension (90°) and mixed mode (30°, 60°) in the Arcan fixture. Both the full field displacement and full field strain profiles of the gauge section are investigated using the stereo imaging (3D DIC). The possibility of achieving the ultimate shear strength in the specimen or the plastic buckling (out-of-plane deformation) of the specimen during the in-plane shear test is explored at the beginning. In the absence of out-of-plane deformation, the material behavior is studied at different loading angles, while the other sets of experiments are focused towards understanding the structural behavior of thin metal sheets. The experimental observations are also compared with the finite element simulation and excellent similarity is observed.

Pure mode axis and the electromechanical coupling coefficients of the 0.67Pb(Mg1/3Nb2/3) O3-0.33PbTiO3 single crystal

Pure mode axes of the 0.67Pb(Mg1/3Nb2/3)O3-0.33PbTiO3 (PMN-0.33PT) single crystals are investigated by slowness surfaces method. It is found only the Z-axis is a pure mode axis. The piezoelectricically stiffened Christoffel equation of the PMN-0.33PT crystal is solved in the rotating coordinate system. All of the single acoustic modes of thickness vibration are obtained. For the pure longitudinal mode of Z-cut crystal, the electromechanical coupling coefficient is up to 0.82. However, it is only 0.34 for the pure shear modes of X-cut or Y-cut crystal. It is along the pure mode axis that the maximum electromechanical coupling coefficients can be achieved.