Multiaxial Stress States Research Articles

A Simple Calibrated Ductile Fracture Model and Its Application in Failure Analysis of Steel Connections

A new fracture model is developed to predict the ductile fracture of structural steel under multiaxial stress states. First, the Lee–Mear void growth theory is used to establish the quantitative relationship between the stress triaxiality and material’s ductility. A stress triaxiality dependence function, which accounts for the material’s strain hardening, is derived from modifying the dilatation rate of a spherical void in a typical unit cell. Subsequently, the Tresca failure model is used in conjunction with the Swift hardening law to establish a Lode dependence of fracture strain. Then, the theoretical formula of the new fracture model is obtained by combining both stress triaxiality and Lode angle dependence functions. The proposed fracture model has a unique advantage: i.e., this model has only two material parameters. These two parameters can be easily calibrated through a simple standard coupon test, which significantly reduces the difficulty of model calibration work and facilitates its application in practical engineering. In order to verify the new fracture model, the test results of five types of Q460 steel specimens were used to calibrate the model parameters. The prediction accuracy of the new model is then checked by calculating the average error between the test results and the predicted fracture strain envelope. Finally, the new fracture model was applied in the numerical analysis of two types of steel connections. The validation of the proposed fracture model is verified by comparing the load–displacement curve and failure modes of the steel connections obtained from both test and numerical analysis.

A thermodynamically consistent finite strain phase field approach to ductile fracture considering multi-axial stress states

Phase field models for ductile fracture have gained significant attention in the last two decades due to their ability in implicitly tracking the nucleation and propagation of cracks. However, most crack phase field formulations for elastoplastic solids focus only on the effects of plastic deformation, and do not consider the different multi-axial stress states that may arise in practical designs. In this work, a thermodynamically consistent phase field approach coupled with finite strain plasticity, considering multi-axial stress states is presented. In order to account for the coupling between plasticity and stress states, the Stress-Weighted Ductile Fracture Model (SWDFM) is utilized. The SWDFM represents a criterion for predicting ductile crack initiation under both monotonic and cyclic loadings based on histories of an internal plastic variable, stress triaxiality, and the Lode angle parameter. The excellent performance of the SWDFM for predicting ductile crack initiation motivates for its incorporation into a phase field approach for predicting both crack initiation and propagation through degradation of the fracture toughness. Moreover, based on the second law of thermodynamics, exact requirements are imposed on the rate at which the fracture toughness can evolve. A novel function for degrading the plastic yield surface during the evolution of damage is introduced. This function, in line with experimental observations, leads to an accumulation of plastic deformation in damaged regions of a solid, and avoids numerical instabilities arising from concentrations of large plastic deformations in severely damaged regions. For validating the proposed model, results of computational simulations are compared to data from selected tests considering different multi-axial stress states. Comparisons of the numerical results with data from laboratory experiments demonstrate the capabilities of the proposed framework.

Interfacial-constraint-mediated pyramidal slip of hexagonal titanium at room temperature

The present study was devoted to investigating the deformation behavior of titanium under interfacial constraints imparted by a heterogeneous multilayered structure. Our results demonstrated the operation of pyramidal slip within Ti layers despite its Schmid factor being lower than that of prismatic or pyramidal <a> slip. Such a behavior was attributed to the role of strong interfacial constraint, and rationalized by the use of the modified Schmid factor in consideration of multiaxial stress state.

An elastoplastic damage model of concrete under cyclic loading and its numerical implementation

A novel elastoplastic damage model describing the complex mechanical behaviors such as stiffness degradation and irreversible deformation of concrete under cyclic loading is constructed and the complete procedure for numerical implementation is presented. To solve the key problems including multi-axial stress states, asymmetry in tension and compression and conversion between tension and compression under cyclic loading, a series of approaches are put forward. A scalar equivalent strain based on the Hsieh-Ting-Chen strength criterion in the framework of strain space is used to convert the complex multiaxial stress state to the simple uniaxial one. Correspondingly, the equivalent strain obtained by the characteristic strength curve addresses the asymmetry in tension and compression, so that the stress–strain relationship in both uniaxial tension and uniaxial compression can be represented by the same curve, and a single damage scalar is available to characterize both tensile damage and compressive damage. To overcome the difficulty of conversion between tension and compression owing to the non-negative equivalent strain, a net equivalent strain is defined to keep the curve proceeding in the first quadrant under reverse loading. Meanwhile, a nominal damage variable is proposed to ensure that the reloading curve can return to the original stress–strain envelope. A new framework of the model with a concise mathematical form has been numerically implemented and is independent of the selection of fundamental governing equations. Typical experimental tests involving three-point bending test, mixed-mode bending test, cyclic uniaxial test, and reciprocating loading test are used for verification. The results calculated by the proposed model are all in good agreement with the tests. As a result, the correctness and reliability of the novel model are demonstrated.

Fatigue Lifetime Analysis of a Bicycle Frame Made by Additive Manufacturing Technology from AlSi10Mg

The development of additive manufactured metals is in the transition phase, from research into the technology of 3D printing and the resulting properties of the metals towards their use in industrial practice. The article analyses the possibilities of producing bicycle frames using 3D printing. The stresses in a bicycle frame are analysed for the measured load spectra and FEM simulation. The approach to the fatigue life assessment of the bicycle frame is based on directly measured load multipliers and detailed FEM simulation with the subsequent calculation of fatigue damage in the individual planes of the critical point of the frame respecting the multiaxial stress state. The scatter of the cyclic properties of the AM material is considered by a statistical approach. The operational fatigue lifetimes of a frame made by 3D printing and one of conventional technology are compared.

Investigation on Homogeneous Modeling of Gyroid Lattice Structures: Numerical Study in Static and Dynamic Conditions

The TPMS (triply periodic minimal surface) are receiving great attention for production of open cell scaffold structures, for example in biomedical applications. In this paper stretch-dominated lattice structures have been considered. The Gyroid cell made of epoxy resin by DLP technology was analyzed. The compression test results in quasi-static (10-3 s-1) and dynamic (4x102 s-1) conditions have been used to compute the macroscopic cellular material properties by the homogenization methods. Finally, in order to evaluate the behaviour of the unit cell under multi-axial stress state, combined shear-compression tests have been carried out as well.

A Damage Model of Concrete including Hysteretic Effect under Cyclic Loading.

A novel damage model for concrete has been developed, which can reflect the complex hysteresis phenomena of concrete under cyclic loading, as well as other nonlinear behaviors such as stress softening, stiffness degradation, and irreversible deformation. The model cleverly transforms the complex multiaxial stress state into a uniaxial state by equivalent strain, with few computational parameters and simple mathematical expression. The uniaxial tensile and compressive stress–strain curves matching the actual characteristics are used to accommodate the high asymmetry of concrete in tension and compression, respectively. Meanwhile, an unloading path and a reloading path that can reflect the hysteresis effect under cyclic loading of concrete are established, in which the adopted expressions for the loading and unloading characteristic points do not depend on the shape of the curve. The proposed model has a concise form that can be easily implemented and also shows strong generality and flexibility. Finally, the reliability and correctness of the model are verified by comparing the numerical results with the three-point bending beam test, cyclic loading test, and a seismic damage simulation of the Koyna gravity dam.

Experimental Study and Theoretical Analysis on the Compression-Shear Multiaxial Mechanical Properties of Recycled Concrete.

Recycled concrete, which is formed by replacing coarse aggregates in ordinary concrete with recycled aggregates (RA), is of great significance for the secondary utilization of waste building resources. In civil engineering, concrete structures are sometimes subjected to a compression–shear multiaxial stress state. Therefore, research on the compression–shear multiaxial mechanical properties of recycled concrete plays an important role in engineering practice. To explore the effect of RA replacement rate on the compression–shear properties of recycled concrete, an experimental study was carried out using a compression–shear testing machine and considering five RA replacement rates and five axial compression ratios. Consequently, the failure modes and mechanical property parameters under different working conditions were obtained and were used to analyze the effects of RA replacement rate and axial compression ratio on the shear stress of recycled concrete. Eventually, the following conclusions were reached: With the growth of axial compression ratio, the shear cracks exhibit a developing trend along the oblique direction, and the friction traces on the shear surface are gradually deepened. As the replacement rate increases, the number of shear cracks is gradually increased, accompanied by increasing broken fragments falling off from the shear interface. Since the action of the axial compression ratio can effectively improve the mechanical bite force and friction on the shear interface of recycled concrete, as the axial compression ratio increases, the shear stress is gradually increased. On the other hand, due to the initial damage of RA and its weak adhesion with cement mortar, the shear stress is gradually reduced with the increase of RA replacement rate. Meanwhile, the increase in shear stress shows a gradually decreasing trend with the growth of axial compression ratio. Specifically, for the RA replacement rates of 0% and 100%, the shear stress increased by 4.06 times and 3.21 times, respectively, under the influence of the axial compression ratio. Under different axial compression ratios, the shear stress was reduced by 43~46%, due to the increase of RA replacement rate. In addition, based on the octahedral stress space and the principal stress space, a compression–shear multiaxial failure criterion and shear stress calculation model for recycled concrete were proposed, by considering the effect of the RA replacement rate. The outcomes of this research are of great significance for engineering applications and the development of recycled concrete.

COLUMN CONFINEMENT WITH TEXTILE-REINFORCED CONCRETE (TRC)

Textile reinforced concrete (TRC) is an innovative composite material consisting of a fine-grained concrete matrix and a textile reinforcement. Due to the corrosion-resistant reinforcement, the concrete cover, which is necessary for reinforced concrete constructions, can be reduced. Combining the tensile mechanical properties of carbon fibers with the compressive strength of fine-grained high-strength concrete, TRC can be seen as an efficient alternative to the previous reinforcement and strengthening measures for concrete columns. By confining the column with TRC, the lateral expansion of the concrete can be impeded. The resulting multiaxial compressive stress state allows to enhance the concretes compressive strength. The aim of this study is the investigation of various influences on the achievable strengthening effect. With the help of experiments on TRC, reinforced columns with circular cross-section mechanical property and constraint mechanism under uniaxial compression were documented and analyzed. Based on the test results, stress distribution and failure mechanisms of the reinforced specimens are studied. Furthermore, the load-displacement relationship of strengthened members is investigated. The effect of the ratio of textile reinforcement, section dimension and concrete strength on the ultimate strength of strengthened members is also evaluated.

Shear property measurement of additively manufactured continuous fibre reinforced plastics by in-plane torsion testing

In-plane shear properties are essential for calculating the plane stress state of composites. Test results for in-plane shear properties of fibre-reinforced polymers (FRPs) are generally obtained with methods that generate multiaxial stress states, and no simple shear response is measured. In this paper, the in plane torsion test method is applied to additively manufactured (AM) continuous FRPs. With this method, planar simple shear loading is achieved for a dedicated, spiral lay-up of the AM specimen. Using digital image correlation, surface strains were obtained for an observed section of the specimen, and shear stress–strain curves were extracted for fibre bundles, co-extruded thermoplastic material, and the composite of both. Shear stiffness and shear strength values are yielded for representative surface areas. Furthermore, the fracture behaviour in shear is discussed. The co-extruded thermoplastic filler material is shown to be the phase where cracks progress is most likely, however as some fibre bundles are split, these can be bridged by the crack. In conclusion, the method is well suited for determination of shear properties of AM continuous FRP material, giving consistent results for the test sample.

COLUMN CONFINEMENT WITH TEXTILE-REINFORCED CONCRETE (TRC)

Textile reinforced concrete (TRC) is an innovative composite material consisting of a fine-grained concrete matrix and a textile reinforcement. Due to the corrosion-resistant reinforcement, the concrete cover, which is necessary for reinforced concrete constructions, can be reduced. Combining the tensile mechanical properties of carbon fibers with the compressive strength of fine-grained high-strength concrete, TRC can be seen as an efficient alternative to the previous reinforcement and strengthening measures for concrete columns. By confining the column with TRC, the lateral expansion of the concrete can be impeded. The resulting multiaxial compressive stress state allows to enhance the concretes compressive strength. The aim of this study is the investigation of various influences on the achievable strengthening effect. With the help of experiments on TRC, reinforced columns with circular cross-section mechanical property and constraint mechanism under uniaxial compression were documented and analyzed. Based on the test results, stress distribution and failure mechanisms of the reinforced specimens are studied. Furthermore, the load-displacement relationship of strengthened members is investigated. The effect of the ratio of textile reinforcement, section dimension and concrete strength on the ultimate strength of strengthened members is also evaluated.

FEM simulation of thermo-mechanical stress and thermal fatigue life assessment of high-speed steel work rolls during hot strip rolling process

Work rolls used for hot strip rolling undergo the cyclic sequence of heating-cooling over the roll surface due to contact with the hot strip and the following cooling systems during every rolling revolution. Severe temperature gradient and thermal stress caused by cyclic heating-cooling loading are dominant factors for thermal fatigue failure of work rolls. Therefore, investigations on temperature and thermal stress-strain are essential for understanding the thermal fatigue of work roll. In this study, a thermo-mechanical analysis with elastic-plastic material parameters via a simplified finite element model is carried out to compute the stress-strain range experienced by the work roll during rolling and idling. Then, a model with the initial crack in the roll surface considering different depths and a model with the hot strip is conducted to better understand the thermal behaviors of the work roll during hot rolling respectively. Furthermore, the thermal fatigue life of work roll is assessed based on the modified Coffin-Manson relation, considering the effect of multi-axial stress state and temperature-dependent material properties caused by temperature fluctuations in work roll during hot rolling.

An improved rainflow counting method for multiaxial stress states using the minimum circumscribed circle method to identify shear stress ranges

Most of the rainflow counting methods are developed for uniaxial stress states. In this paper, a new method for rainflow counting of multiaxial stress states has been proposed. The proposed method is a two-step procedure based on a modified three-point ASTM uniaxial rainflow counting algorithm where normal stress ranges are identified along with start and end indexes of each range. For each identified cycle, shear stress ranges are evaluated based on cycle start and end points using the minimum circumscribed circle method. The proposed algorithm is compared to two commonly applied multiaxial cycle counting methods on simulated and experimental data.

Eccentric punching tests on column bases – New insights into the inner concrete strain development

In the past, the punching shear behavior of centrically loaded column bases has been predominantly investigated even though eccentric loads frequently occur in engineering practice. To consider this corresponding uneven shear stress distributions around the column, many design approaches define coefficients to increase the acting load. Due to the limited test data for eccentric punching tests, an assessment of the design approaches is not reliably possible. To fill this gap of experimental test results, four centrically loaded and fourteen eccentrically loaded punching tests were conducted to analyze the effects of systematically graded load eccentricities.The tests reveal a significant influence of load eccentricity on the punching shear capacity and the load-bearing behavior. With increasing eccentricity, the crack formation shifts to the higher loaded side going along with an incompletely developed punching cone. Innovative measurements of the strains in the slab allow to analyze the circumferential multi-axial stress state inside the concrete. In contrast to centrically loaded column bases, this compression ring does not fully develop under eccentric loads. Based on these measured tangential strains, an experimental approach for describing the influence of the load eccentricity on the punching shear strength is derived and compared with the design approaches of Eurocode 2, Model Code 2010 and the stable version of the next generation of Eurocode 2. Overall, the results indicate optimization potential for more advanced design provisions of column bases with eccentric loads.

Validation of crack initiation model by means of cyclic full-scale blade test

Wind turbine rotor blades are subject to highly dynamic loads and designed for life cycles of at least 20 years, which means that materials are subjected to high-cycle fatigue. Fatigue is a design-driving loading for current and future blades. Bond lines of blades are exposed to a multi-axial stress-state due to the anisotropic thin-walled blade structure and curved, tapered, twisted, and airfoil-shaped blade geometry. To eliminate undesirable failure modes and thus increase the reliability of wind turbine rotor blades, standards and guidelines recommend that the multi-axial stress-states be taken into consideration for the limit state analysis. In addition, thermal residual stresses that develop during manufacture can have a significant impact on the fatigue life of the bond line. By means of a cyclic full-scale blade test of a commercial 81.6m long offshore blade, we validate a crack initiation model, which takes into account multi-axial thermal and mechanical stress-states, as well as the probabilistic stress-life, to predict the edge of crack initiation in the adhesive as well as the span-wise position. Both observations agreed well with the simulations. All residual normal stress components and cross-sectional plane shear stress made up the major part of the mean equivalent stress, while the mechanical stress amplitude components - longitudinal, peel, and cross-sectional plane shear stress - made up the major part of the equivalent stress amplitude.

Simulation of concrete structures deformation affected by alkali–silica reaction considering environmental conditions and multiaxial stress state

In this study, the expansion and deformation of alkali–silica reaction (ASR)-affected concrete structures under natural environment and multiaxial stress state are predicted. The performance of the ASR model proposed in previous research is quantitatively investigated in terms of relative humidity, multiaxial stress, and temperature dependencies based on experimental results. The simulation results indicate that the relative humidity-dependent expansion caused by the ASR can be simulated effectively by slightly modifying the relative humidity threshold in the model. In a simulation focusing on stress dependency, the insufficient consideration of the relationship between compressive stress and ASR gel absorption into pores in the model by previous research resulted in discrepancies between the simulation and experimental results. The performance of the model by previous research in simulating temperature dependency is improved by referring to the relationship between the expansion rate and temperature recorded from specimens exposed to the real environment. An exposure experiment of reinforced concrete (RC) slab on steel girders is simulated using the modified model. The results show that the modified model can reproduce the tendency of three-dimensional deformation of RC slab, while model improvement considering time-dependent and stress-dependent phenomena should be needed for long-term quantitative predictions.

Theoretical and Experimental Study considering the Influence of T-Stress on the Fracture Behavior of Compression-Shear Crack

The influence of the nonsingular stress term (T-stress), existing in the Williams expansion of the crack tip stress field, on the fracture behavior of the compressive-shear crack is comprehensively considered in this paper. According to the stress boundary conditions on the crack surfaces, the theoretical solution of the stress field around the closed crack tip is established using the complex potential theory, which includes not only the singular term containing the stress intensity factor KII but also three nonsingular terms (T-stress: Tx, Ty, and Txy) without KII. Then, the differences between tangential stresses and shear stresses at the crack tip obtained in the cases with and without T-stress are compared, respectively. Outcome indicates that there are tangential tensile stress and compressive stress zones at the crack tip when considering T-stress, while only the former exists when ignoring T-stress. In the case of considering T-stress, an improved crack initiation criterion is proposed, where the maximum tangential tensile stress and maximum shear stress are utilized simultaneously to predict the crack initiation and failure mode under the multiaxial compression stress state. Besides, the triaxial compression tests were carried out on the prismatic rock-like material samples with a central crack, and the effectiveness and validity of the proposed criterion are verified by comparing the experimental results and theoretical predictions. It reveals that the proposed criterion can reliably predict the crack initiation angles and failure modes with higher accuracy than traditional fracture criterion.

Evaluation on Flexibility of Phenomenological Hardening Law for Automotive Sheet Metals

Constitutive modeling of sheet metals involves building a system of equations governing the material behavior under multi-axial stress states. In general, these equations require a hardening law that describes the stress-strain relationship. This study provides a thorough examination of the existing phenomenological hardening laws in the literature. Based on their ordinary differential equations, special efforts were made to discuss the degree of flexibility of these hardening laws. Four new phenomenological hardening laws were proposed during the discussions to capture the stress-strain relationship of automotive sheet metals, such as aluminum alloy and steel sheets. Then, applications of 18 hardening laws for fitting the uniaxial tensile stress-strain data of 12 automotive sheet metals were thoroughly compared. The comparisons reveal that the proposed hardening laws capture well the experimental stress strain data of all examined materials. Compared to several combined hardening laws, the proposed functions have comparable flexibility but require fewer parameters.

Distributed fiber optic sensors for measuring strains of concrete, steel, and textile reinforcement: Possible fields of application

AbstractThe article describes measurements of strains of concrete, steel and textile reinforcement with distributed fiber optic sensors (DFOS). The technology of distributed strain measurements gains currently increasing attention within the civil engineering field and indeed the DFOS can be applied in various measurement scenarios providing results and insights which were not possible before. Within this article, the fibers and adhesives that are most commonly used are compared and several measurement scenarios and their results are described, including precise strain measurements with high resolution as well as measurements on large‐scale specimens. Concrete strains were measured in a multiaxial compression stress state and also during setting and hardening and in flexural tests. Strains of the steel and textile reinforcement were monitored along the bond zone and also in flexural tests. Finally, cracking patterns were observed and compared with digital image correlation methods. Validated examples of applications of DFOS in laboratory work are described.

Creep characterization and modelling of ordinary refractory ceramics under combined compression and shear loading conditions

Creep behaviour of ordinary refractory ceramics is evidently asymmetric under uniaxial tension and compression. In service, they are often exposed to multiaxial stress states. In the present paper, the modified shear test specimens were applied for a creep study in the shear-compression zone of the p-q diagram, and the pure shear creep parameters following the Norton-Bailey strain hardening equation were inversely identified in combination with a weighting function between pure shear and uniaxial compressive conditions. The weighting function was implemented in an in-house asymmetric creep constitutive model. The experimental curves can be well predicted with identified parameters of the asymmetric creep constitutive model. It shows that the shear creep of ordinary refractory ceramics is evidently different to uniaxial compressive/tensile creep. Consideration of shear creep in the thermomechanical modelling of industrial vessels increases the accuracy of simulation results and supports the lining concept optimization investigation.