Combined Stress State Research Articles

Anisotropic mechanics of cell-elongated structures: Finite element study based on a 3D cellular model

Cell-elongated structures present designable anisotropic behaviors by controlling the ratio and angle of elongation, but the relationship between geometric anisotropy and mechanical anisotropy remains poorly understood. In this study, a construction method based on the 3D Voronoi technique is employed to generate cell-elongated structures with different elongation ratios and angles, and their anisotropic compression behaviors are investigated using a 3D cellular model. The stress–strain curves can be categorized into four stages, including elasticity, initial collapse followed by strain-softening, plateau, and densification, which are accurately described by a statistical constitutive model. Our finding reveals that the mechanical properties and deformation modes of the cell-elongated structures are significantly influenced by the anisotropic angle. At an anisotropic angle of 0°, randomly distributed collapse bands due to shell buckling interact with each other during compression, enhancing the load-carrying and energy-absorbing capacities. Conversely, at 90°, the cells deform primarily through a stable bending mode, leading to reduced stress and a lower Poisson’s ratio. At 45°, collapse bands appear on both sides of the sample with rotation and buckling being the dominant deformation mode, resulting in a sandwich-like structure featuring an uncollapsed central zone due to a combined compression–shear stress state. Compared with the isotropic foam, the structure elongated in thickness direction exhibits a notable increase in impact resistance under a spherical bullet. This work demonstrates the potential to engineer anisotropic cellular materials with tailored mechanical properties and deformation modes through strategic geometric anisotropy design.

Feasibility Study of Experimental Protocol for the Time-Dependent Mechanical Response of Synthetic Tibia.

In this research, an experimental biomechanics construct was developed to reveal the mechanics of distal tibial fracture by submitting synthetic tibiae to cyclic loading, resulting in a combined stress state due to axial compression and bending loads. The synthetic tibia was fixed at the knee but allowed to rotate in the coronal and sagittal planes at the ankle. The first three loading regimes lasted for 4000 cycles/each, and the final until ultimate failure. After 12k±80 cycles, the observed failure patterns closely resembled distal tibial fractures. The collected data during cyclic loading were fitted into a phenomenological model to deduce the time-dependent response of the synthetic tibiae. Images were also collected and analyzed using digital image correlation to deduce the full-field state of strain. The latter revealed that longitudinal strain contours extended in the proximal-distal direction. The transverse strain contours exemplified a medial-to-lateral distribution, attributed to the combined contributions of the Poisson's effect and the flexural deformation from axial and bending components of the applied load, respectively. The experimental construct, full-field characterization, and data analysis approaches can be extended to elucidate the effect of different fixation devices on the overall mechanical behavior of the bone and validate computational models in future research.

Effect of shear stresses on fibre direction tensile failure using a new simple and reliable test method with thin plies

A new method of creating in-plane combined tension-shear stress states using only tensile loading is proposed. Thin-ply angle-ply carbon/epoxy laminates are sandwiched between unidirectional glass layers to eliminate any stress concentration around the samples ends and gripping zone. Use of the thin plies successfully suppresses early occurrence of other modes of failure i.e. matrix cracking and free-edge delamination, so the first mode of failure is fibre failure in the angle-ply carbon sub-laminate. Compared with other methods of creating combined tension-shear stresses, the proposed technique has a simpler geometry, is significantly easier and cheaper to manufacture and test. Therefore, it provides more repeatable low-scatter experimental results.The obtained experimental results showed that the presence of in-plane shear stresses did not have a significant impact on the tensile fibre-direction failure strain of the tested carbon/epoxy laminate, suggesting that even at high shear stresses, the longitudinal tensile strength of the carbon/epoxy laminate is not significantly reduced.

Evaluation of True Bonding Strength for Adhesive Bonded Carbon Fiber-Reinforced Plastics.

Carbon fiber-reinforced thermoplastics (CFRTPs) have attracted attention in aerospace because of their superior specific strength and stiffness. It can be assembled by adhesive bonding; however, the existing evaluation of bonding strength is inadequate. For example, in a single-lap shear test, the weld zone fails in a combined stress state because of the bending moment. Therefore, the strength obtained experimentally is only the apparent strength. The true bonding strength was obtained via numerical analysis by outputting the local stress state at the initiation point of failure. In this study, the apparent and true bonding strengths were compared with respect to three types of strength evaluation tests to comprehensively evaluate bonding strength. Consequently, the single-lap shear test underestimates the apparent bonding strength by less than 14% of the true bonding strength. This indicates that care should be taken when determining the adhesion properties for use in numerical analyses based on experimental results. We also discussed the thickness dependence of the adhesive on the stress state and found that the developed shear test by compression reduced the discrepancy between apparent and true strength compared with the single-lap shear test and reduced the thickness dependence compared with the flatwise tensile test.

Computation of the fracture probability and lifetime of all ceramic anterior crowns under cyclic loading - An FEA study.

To predict the lifetime and fracture probability of anterior crowns made of a lithium disilicate glass-ceramic (IPS e.max CAD, LD, Ivoclar Vivadent, Liechtenstein) and a zirconia-containing lithium silicate glass-ceramic (Celtra Duo, ZLS, Dentsply Sirona, USA) under cycling loading. Three-point bending tests were conducted to measure the viscoelastic parameters. These parameters are used to compute the residual stresses of the anterior crown after crystallization. In the next analysis, the cyclic loading on the anterior crown was calculated. Based on this combined stress state (residual stress and stress state due to external cyclic loading), the life cycle and fracture probability of the anterior crown was calculated using the CARES/Life software. Finally, fatigue experiments were carried out to compare and validate the results of the computations. Although a sound qualitative comparison of the lifetime of both materials can be done using this methodology, the calculated fracture probability of the anterior crown for both materials was very low in comparison with the fatigue test results using the fatigue parameters determined from the experiments. In order to achieve good correspondence with the experimental results, the SCG exponent n for both materials should be modified by a correlation factor of 0.38. Using this modified computational strategy, the results of the time-consuming fatigue tests for dental glass-ceramics can be closely predicted. This methodology can be integrated into the development process of new glass-ceramic materials in order to save time and costs.

Creep-Fatigue Life Property of P91 Welded Piping Subjected to Bending and Torsional Moments at High Temperature

Abstract In recent years, the role of thermal power plants has shifted from providing a baseload to providing supplemental supply to compensate for fluctuations in the output of renewable energy sources. Thus, the operation of these plants involves frequent startup and shutdown cycles, which lead to extensive damage caused by creep and fatigue interactions. In addition, the piping utilized in thermal plants is subjected to a combined stress state composed of bending and torsional moments. In this study, a high-temperature fatigue testing machine capable of generating such a bending-torsional loading was developed. Creep-fatigue tests were conducted on P91 steel piping with weldment. The results clarified that the creep-fatigue life was reduced by the superposition of the torsional and bending moments and that it was further reduced by a holding load. It was shown that the creep-fatigue life of piping with weldment can be estimated accurately using the equivalent bending moment, which is composed of the torsional and bending moments. It was also confirmed that crack occurred in the heat-affected zone (HAZ) of the welded part, which has been often observed in actual thermal power equipment. From the finite element analysis, it was identified that cracking was initiated in the HAZ due to the accumulation of creep strain and increase in the hydrostatic pressure component during a holding load.

Coupled versus energetic nonlocal failure criteria: A case study on the crack onset from circular holes under biaxial loadings

The phenomenon of brittle crack onset stemming from a circular hole in an infinite plate subjected to remote biaxial loading is herein investigated. A thorough analysis on the influence of the loading biaxiality reveals the existence of a wide casuistry in the sign and trend distributions of the stress field and Stress Intensity Factor, thus rendering it an exhaustive case study for assessing different failure criteria. Subsequently, three different approaches are used to determine the biaxial safety domains, two of which rely on the coupling of stress and energy conditions for failure, namely Finite Fracture Mechanics and Cohesive Zone Model, plus the purely energy-driven Phase Field model of fracture. Noteworthy, Finite Fracture Mechanics predicts the existence of a region in the loading space where failure is exclusively governed by the energy condition. Likewise, it is mathematically proven that the system of equations governing Dugdale's Cohesive Zone Model is equivalent to the first-order minimization condition of the energy balance, the resultant predictions being fairly close to those obtained by Finite Fracture Mechanics. Lastly, the Phase Field model of fracture is numerically implemented in the context of Finite Elements while paying special attention to the choice of the energy decomposition, whereof two are implemented: No-Decomposition and No-Tension decomposition. Specifically, the latter showcases satisfactory agreement with both Finite Fracture Mechanics and Dugdale's Cohesive Zone Model, thus posing a solid contender for studying complex fracture scenarios upon combined tension-compression stress states.

Evaluation of the Occurrence of Initial Failures from Stress Concentrators in Welded Joints and Structural Elements

Introduction. Data on the occurrence of initial failures obtained through testing on standard samples cannot always be extrapolated to real welded joints and structures. This is due to the difference between the concentrators in the joints, because after welding there is a significant structural and mechanical heterogeneity of the heat-affected and stress concentrator zone. Extended, deep concentrators are considered as crack-like defects, at whose vertices a volumetric, multiaxial stress state is formed. The paper addresses the issue of constructing critical diagrams of the onset of the limiting state at the concentrator vertex, which depends on the level of external load and the theoretical concentration coefficient.Materials and Methods. Analytical methods were used to study the stress state. The literature on the topic was analyzed. The features of proven physical models and patterns of behavior of materials were taken into account. The characteristics of steel alloys were taken from open sources and summarized in a tabulated form. Nonlinear equations were solved in Matlab applications. The diagrams constructed by the authors enable to track the correlation of the dangerous level of the theoretical stress concentration factor and the level of external load. Curve Fitting Toolbox Matlab was used to design the graphic part of the work.Results. The characteristic of damage from stress concentrators in welded joints was given. The crack propagation in the fusion zone was shown. The conditions stimulating and inhibiting destruction were indicated. The theoretical stress concentration factor α𝑇 was specified. It was shown how this indicator depended on the width, the height of the seam and the thickness of the welded part. Acute stress concentrators with theoretical concentration factor αт= 5…14 and more were studied. For this case, an approximating formula was given that took into account the maximum stress in the concentrator in the first half cycle, the initial deformation, and the load ratio. Through those elements, an indicator of an increase in maximum stresses was set depending on the number of loading cycles. The flow condition, the stress state, and the overvoltage factor, which took into account the increase in the first principal voltage for a combined stress state, were analytically shown. A model of the critical state at the apex of an acute stress macro concentrator was described. It was presented as the dependence of the relative stresses of the initiation of destruction σн𝑏𝑐/σ0,2 on the concentrator. Possible variations of this model were analyzed. The dependences of relative values σ𝐻𝑏𝑐⁄σ0,2 on the theoretical concentration factor α𝑇𝑏𝑐=α𝑇 were presented. To check the physical adequacy of this model, graphs were constructed that reflected changes in the relative stress of the external load at a critical state at the stress concentrator apex. The inevitability of bifurcation as a result of the studied processes was validated. Two directions of further development of events were indicated: brittle destruction and loss of stability of the stressed state with the transition to an increase in plastic deformations. The moment of bifurcation was defined as a critical state in the focus of the concentrator.Discussion and Conclusion. The analysis and calculations performed within the framework of the presented scientific work enabled, in particular, to draw conclusions about the role of key factors of the processes under study. It was established, for example, that the operation of a steel alloy at a high theoretical stress concentration factor depended on the characteristics of the stress state. In a rigid state, it was possible to inhibit shear deformation and the onset of the limiting state at a lower value of the theoretical stress concentration factor. With the usual strength of steel (in comparison to high), a greater impact of the volume of the stress state on the value of the theoretical stress concentration factor was recorded. The probability of failure depended on the resistance of the material to the growth of a macrocrack. In future research, it is possible to refine analytical models and results, evaluate effective stress concentration factors.

Off-Axis Tension Behaviour of Unidirectional PEEK/AS4 Thermoplastic Composites

An experimental method for non-standard off-axis tension tests of unidirectional composites is developed. A new oblique end-tab is designed to eliminate stress concentration and in-plane bending moment induced by off-axis tension loading. Finite element analysis and experiments on Polyetheretherketone (PEEK)/AS4 unidirectional thermoplastic composites (CFRTP) were conducted to evaluate the effectiveness of the proposed testing method. Simulation and test results demonstrate that the use of oblique end-tabs eradicates stress concentration and bending movements. The digital image correlation (DIC) method was used to help investigate the full-field tension/shear coupling deformation response of the off-axis specimen. Test results show significant nonlinear behaviour and inhomogeneous strain distribution under tension/shear combined stresses. A fractographic study was carried out to study the damage mechanisms under a tension/shear combined stress state. Specimens with 30°, 45° and 60° off-axis angles, fail in tension/shear mixed failure mode. Fracture surface morphology indicates that matrix plastic deformation and ductile drawing under tension/shear coupled stress state induced the nonlinear stress-strain response.

Bending behaviours of load-carrying fillet welds around misaligned hollow structural sections

Misaligned hollow structural section (HSS) chords have gained increasingly application in the tubular joist structures connecting panelised façades. Despite the fillet welds are known to be efficient in connecting the HSS structures, the bending behaviours and fracture characteristics of welded misaligned HSSs have not been clearly understood for their engineering practice. This paper presents the results of an experimental and finite element (FE) modelling study with focus on the combined stress states of the misaligned HSS and the critical weld throat plane in its connecting welds. The configurations for the corner connection and the interior wide connection were compared in terms of their failure modes and load–deflection response. A theoretical analytical approach for predicting the combined stress of the misaligned HSS chord and the fillet weld in the connection subjected to flexural, shear and torsional loading is proposed and shown to achieve a good correlation. Based on the results of validated FE models, the traction stresses of fillet welds with appropriate allowance of the weld eccentricity induced secondary moment are demonstrated to give a better replication of the stress distribution of the critical weld throat plane. Finally, it has been found from a FE parametric analysis that the local stress concentration at the critical weld throat plane can be significantly amplified with increased weld flank angle, decreased HSS chord thickness-to-width ratio, increased misalignment angle of HSS chord or reduced relative weld leg length, in which the last two influential factors notably contribute to the elevation of stress concentration.

Material Modeling of Perforated Sheet Metals with Different Hole Arrangements by Homogenization Method

The homogenization method is effective for analyzing macroscopic mechanical properties from the substructure of a material. In perforated sheet metal, macroscopic mechanical properties depend on the pattern of hole arrangement. In this study, the macro–plastic properties of perforated sheets with 60° standard staggered and 90° square arrangements are modeled. Biaxial stress is applied to the unit cells given the periodic boundary condition, and the contours of equal plastic work are obtained. The yield surfaces of the perforated sheets on the tension–compression combined stress state are strongly affected by the hole arrangement. To model the yield surface, a yield function for the rotational symmetry peculiar to the perforated sheet is proposed. The yield surfaces are modeled using the CPB2006 yield function that takes into consideration tension–compression asymmetry. Also, a surface–interpolated differential hardening model is applied to model the changes of yield surfaces. The analysis results obtained using the modeled yield surfaces are compared with the experimental ones obtained on the uniaxial tensile and deep drawing tests. The results of both tests show good agreement.

Ceramic Bonding Interface under Shear–Compression Stress: Ultra-High-Speed Imaging Contribution

The aim of this study is to visualize and characterize by ultra-high-speed imaging (UHSI) the failure phenomena at the resin–ceramic bonding interface of lithium disilicate (LiSi2) samples bonded with gold-standard protocol (Monobond Plus [MB]) and the nontoxic one (Monobond Etch & Prime [MEP]) subjected to mechanical loading. Unprecedented frame rate, image resolution, and recording time were reached by using the most advanced UHSI camera. The finite element analysis (FEA) of the proposed mechanical test confirmed that the specific design of our samples enables a combined shear and compression stress state, prone to test the bonding interface while being close to physiological stresses. Ten LiSi2 samples were pretreated by gold standard (MB, n = 5) and self-etching primer (MEP, n = 5). Axial compression loading gradually increased until catastrophic failure was performed. As shown by the FEA, the angle between the bonding interface and load direction leads to shear–compression stresses at the resin–ceramic bonding interface. Failure was recorded by UHSI at 300,000 fps. All recorded images were analyzed to segregate events and isolate the origin of fracture. For the first time, thanks to the image recording setup, it was observed that debonding is the first event before breakage, highlighting that sample fracture occurs by interfacial rupture followed by slippage and cohesive failure of materials. Failure mode could be described as mixed. MEP and MB showed similar results and behavior.

Off-Axis Compressive Behaviour of Fibre Reinforced Thermoplastic Composites.

This paper presents an experimental investigation on the mechanisms of damage onset and evolution in unidirectional PEEK/AS4 carbon fibre reinforced thermoplastic (CFRTP) composites subjected to off-axis compressive loadings. A test fixture was designed to prevent buckling, splitting, and end collapsing of the specimens during the test. A series of compression tests were conducted with specimens of various off-axis angles. The displacement and strain fields of all specimens during the tests were evaluated by the digital image correlation (DIC) method. In combination with the DIC results, the influence of the off-axis angles on the failure mechanisms and nonlinear stress–strain responses were analysed. The corresponding failure mechanisms were examined by scanning electron microscopy (SEM). The fracture angles of the tested specimens were evaluated and analysed according to Puck’s theory. The off-axis compression failure envelope based on LaRC05 and Hashin criteria was presented and compared to the experimental results. It was shown that the LaRC05 criterion can provide accurate predictions when the off-axis angle is larger than 15°. The complex failure mechanisms were analysed to better understand the effect of ductility of the thermoplastic matrix to the composites. The series of tests provide an experimental failure envelope in combined stress states and can be used for the evaluation of failure theories and the criteria of thermoplastic composites.

Realization of Tensile-Bending Mechanical-Thermal Coupling Fatigue Based on a Uniaxial Tensile-Fatigue Testing Device

Lack of advanced testing technology and instrument restricted development and application of material subjected to multiaxial mechanical-thermal coupling fatigue load. This paper developed the mechanical-thermal coupling tensile-bending combined fatigue testing instrument by modifying the existing uniaxial tensile testing device and the shape of specimens. The thermal loading unit, thermal insulation unit, and temperature monitoring unit were integrated into the tensile testing device to obtain fatigue properties of different temperatures. A single v-notch used to adjust the ratio of bending component to tensile component was prepared on the symmetric specimen to establish the tensile-bending coupling stress state of the minimum cross-section of specimens. The v-notch specimens and conventional symmetrical specimens were used on the modified instrument to test at room temperature to 600 °C. The performance of the modified instrument was verified through the stability of load response, the consistency of fatigue fracture process and displacement response, and the softening trend of material with the increase of temperature. The tensile-bending stress state caused by v-notch was proved through finite element analysis and the stress analysis based on the crack growth morphology. A deep neural network model was established connecting the testing parameters and the tensile-bending combined stress state, and the feasibility of the model was verified by small enough training error and testing error.

A Numerical Approach for Plastic Cross‐Sectional Analyses of Steel Members

AbstractGlobal structural analyses in civil engineering are usually performed considering linear‐elastic material behavior. However, for steel structures, a certain degree of plasticization depending on the member classification may be considered. Corresponding plastic analyses taking material nonlinearities into account are effectively realized using numerical methods. Frequently applied finite elements of two and three‐dimensional models evaluate the plasticity at defined nodes using a yield surface, i.e. by a yield condition, hardening rule, and flow rule. Corresponding calculations are connected to a large numerical as well as time‐consuming effort and they do not rely on the theoretical background of beam theory, to which the regulations of standards mainly correspond. For that reason, methods using beam elements (one‐dimensional) combined with cross‐sectional analyses are commonly applied for steel members in terms of plastic zones theories. In these approaches, plasticization is in general assessed by means of axial stress only. In this paper, more precise numerical representation of the combined stress states, i.e. axial and shear stresses, is presented and results of the proposed approach are validated and discussed.

Modeling of Ductile Fracture for SS275 Structural Steel Sheets

A series of earthquake events give impetus to research on the ductile fracture behavior of steel materials. In the last decades, many fracture models have been developed and utilized in the mechanical or aerospace engineering. Nevertheless, very little application to structural members used in the construction industry has been made due to the lack of a suitable model for the fracture behavior of constructional steel. This paper presents the experimental and finite element (FE) technique to predict ductile fracture in mild carbon structural steel (SS275) sheets, which has been widely used in building structures. The post-necking true stress–strain responses were successfully estimated using the weighted-average method. The Bao and Wierzbicki (BW) model, which requires only two model parameters, was selected for the identification of fracture locus. Each model parameter was calibrated from uniaxial tension and in-plane shear specimens with the aid of digital image correlation (DIC) and finite element analysis. Fracture simulation was then performed and validated based on the experimental results of the specimens under combined tension and shear stress state.

The mechanical behavior of RPC under combined shear and compressive loads

In this study, the shear behavior of reactive powder concrete (RPC) in terms of shear strength and shear slip was studied by direct shear tests on cubic specimens and the influences of water-binder ratio, steel fiber volume ratio and normal compressive stress ratio were investigated. The test results indicated that using a low water-binder ratio and a reasonable fiber content could enhance the shear strength of RPC specimens. The RPC specimen containing steel fiber will not be severed into two individual parts due to the connection of steel fiber. Moreover, the normal stress was the key contribution to the shear strength, and the residual shear capacity was mainly provided by the friction of the shear surface. The cracking of the specimens became more severe but the shear strength in the cyclic horizontal test did not decrease obviously compared with that in the monotonic horizontal test. Applying the twin-shear unified strength theory to the test data, it was indicated that the elliptic curve showed a good agreement. Therefore, the unified twin shear strength theory could predict the proper RPC strength envelope curve under combined compressive-shear stress states.

Material Modelling of Fabric Deformation in Forming Simulation of Fiber-Metal Laminates – A Review on Modelling Fabric Coupling Mechanisms

During forming of complex fiber-metal laminates (FML), compressive stress zones occur. In pure textile forming, these compressive stresses typically lead to extensive wrinkling. In FML forming, however, wrinkling is partly hindered by the metal layers. Thus, combined stress states occur, where compression influences the deformation. In forming simulation, these compressive stresses can lead to erroneous formation of shear bands within the fabric layer, if the deformation behavior is not modelled correctly. Simple fabric models neither consider interactions between roving directions nor model interactions between membrane strains and shear strains. More advanced invariant-based hyperelastic material models are able to capture these interactions, but only consider tension and shear, while disregarding compression. A common assumption is to set the fabric compression stiffness close to zero. Experimentally, the in-plane fabric compression stiffness has not been determined so far. However, in FML forming, the compression stiffness and the combined compression-tension-shear behavior becomes relevant. In this article, the authors summarize and analyze the capacity of state-of-the-art fabric material models to predict the deformation behavior of fabrics under combined loading. Based on these findings, conclusions are drawn for a new macroscopic modeling approach for woven fabrics, including coupling of tension, compression and shear.

Molecular Dynamics Simulation for Evaluating Fracture Entropy of a Polymer Material under Various Combined Stress States

Herein, the stress-state dependence of fracture entropy for a polyamide 6 material is investigated through molecular dynamics simulations. Although previous research suggests that a constant entropy increase can be universally applied for the definition of material fracture, the dependence of stress triaxiality has not yet been discussed. In this study, entropy values are evaluated by molecular dynamics simulations with varied combined stress states. The calculation is implemented using the 570,000 all-atom model. Similar entropy values are obtained independently of stress triaxiality. This study also reveals the relationship between material damage, which is correlated with void size, and the entropy value.

Investigation on three-dimensional failure criterion of asphalt mixture considering the effect of stiffness

In order to reveal the effect of complex stress state on the characteristics of strength and stiffness of asphalt mixture, the self-developed double confining pressure triaxial test method was used in this study. The one-time failure and resilient modulus tests in complex stress state were carried out on the SMA-13 and AC-13 asphalt mixtures widely used in China's asphalt pavement, especially in the combined tensile-compressive stress state. The failure principal stress of material and its stress-strain data under the step loading condition were obtained. The calculation model of resilient modulus in complex stress state and the failure criterion I1-J2 in the principal stress space were established. On this basis, based on the generalized Hooke's law, a three-dimensional strain failure criterion model for asphalt mixture considering the effect of stiffness was also established by the conversion method. The research results can provide experimental and theoretical support for the reasonable selection and resistance calculation of material parameters of asphalt mixture in complex stress state.