Loading Path Dependence Research Articles

Load path dependence for passively and actively confined high-strength concrete

The assumption of load path independence has been instrumental in developing analysis-oriented stress-strain models for FRP-confined concrete. However, there remains no consensus on this assumption when applied to high-strength concrete (HSC). An axial stress gap is typically observed between active and passive confined HSC cases, even when their confinement conditions and deformations are identical. To address the existing research gap, this study conducted experimental tests on a series of HSC specimens under various levels of active and passive confinement. These tests aimed to assess the influence of the stress disparity between the two confinement mechanisms. Cyclic loading was also applied to the confined HSC specimens to derive damage indices (plastic strain, tangent unloading stiffness, and reloading stiffness) and to establish their relationship with the stress gaps. The findings revealed that the stress gap identified from different confinement types increases with the strength of the concrete. It also varies with the axial strain, exhibiting a trend that initially increases and then decreases. The test results further indicated that the presence of this stress difference is a response to internal damage within the concrete. Specifically, under different confinement paths, a reduction in the plastic strain difference that characterizes the damage will lead to a decrease in the stress gap. Moreover, under large deformations, the severe internal damage condition in concrete also reduces the damage differences for HSC experiencing different load paths, which in turn diminishes the stress gap. These insights provide a deeper understanding of how different confinement mechanisms affect the material properties of HSC under various load paths.

Polymorphic phase transition in CoCrNi medium-entropy alloy under impact loadings

Polymorphic phase transition in metallic materials under high pressure is a critical aspect of dynamic properties and has been attracting a great interest. Despite the extensive researches have been made on understanding of this phase transition in traditional single-principal element alloys, little is known about the phase transition in recently emergent multi-principal medium and high entropy alloys, especially compressed under high strain rates. In this work, based on molecular dynamic simulations, three impact loading strategies with distinct loading paths, such as single-shock, double-shock and ramp-wave loading are carried out on the single crystalline CoCrNi medium-entropy alloy (MEA) to investigate the phase transition under high strain-rate compression. Careful characterizations show that the phase transition of CoCrNi MEA is loading-path dependent, as evidenced by the significant differences in macroscopic pressure evolution and microscopic structural phase transition among the samples under various thermodynamic paths. An intriguing pressure “overshoot” is found and demonstrated as the characteristic of the critical structural phase transition from face-centered cubic (FCC) structure to hexagonal-close-packed (HCP) structure mediated by body-centered cubic (BCC) like clusters. We show that such loading-path dependence is attributed to the strain rate and temperature rise in the loading process, which control the evolution of microstructure and deformation field. The inherent correlation between the atomistic process of phase transition and loading strategies results in polymorphic phase transition under high strain rates. These findings shed new light on the nature of impact phase transition of multi-principal alloys.

Tension-compression asymmetry of temperature dependencies in Mg rare-earth alloys

To reveal the tension-compression asymmetry of temperature-dependency in Mg-RE alloys, uniaxial tensile and compression tests followed by microstructural characterizations were performed on a cast Mg-10Gd-3Y-0.5Zr (wt.%) alloy under various temperatures. The results show that this alloy exhibits anomalous temperature effects on mechanical properties (such as tensile strength and plasticity) during tension, while they are not observed during compression tests, demonstrating that the anomalous temperature effects exhibit loading path dependence. The tension-compression asymmetry of the anomalous temperature-dependency associated with variations in twinning. It is believed that these variations in twinning result from the interplay between the inhibitory effect of rare earth elements on twinning and the promoting effects of elevated temperature or a change in the loading path from tension to compression, with the loading path having a stronger promoting influence than the deformation temperature.

Size-dependent yield criterion for single crystals containing spherical voids

A micromechanics-based yield criterion is derived for a porous single crystal containing a random distribution of spherical voids, using homogenization and limit analysis of a hollow spherical representative volume element obeying a strain gradient crystal plasticity model. The criterion captures the effect of plastic anisotropy due to crystallographic slip on a set of discrete slip systems, as well as the void size dependence of yielding. The yield criterion is formally similar to the well known Gurson model for isotropic porous materials, and reduces to existing results in the literature in the limiting case of large void sizes relative to the length scale in the gradient plasticity model. The yield criterion is validated by comparison with rigorous upper bound yield loci obtained using a numerical limit analysis procedure. Predictions for the size dependence of void growth are obtained by integrating the porous plasticity model, and shown to be consistent with the observations from lower scale discrete dislocation dynamics simulations. The loading path dependence of void growth in the size-independent limit are compared with finite element simulations of void growth in a single crystal using the unit cell model.

Path-dependent multiaxial fatigue behavior of A319 aluminum alloy under non-proportional loading conditions

Abstract In the multiaxial low fatigue test study, four multiaxial non-proportional fatigue loading paths were used including rectangular, square, rhombic and circular. The effect of loading condition changes on the fatigue behavior and cyclic damage characteristics of A319 aluminum alloy was investigated by means of stress response curves, stress–strain hysteresis lines, fatigue fracture morphology, and dislocation substructure morphology in combination with material microstructure. The non-proportional hardening behavior exhibits strong loading path dependence, and the fatigue plastic deformation in the torsional direction is greater in the circular and rhombic paths, and the fatigue damage is more severe, resulting in a shorter fatigue life of A319 aluminum alloy. The axial directions under non-proportional multiaxial loading all have tensile and compressive asymmetric behavior. The differences in loading paths result in different fatigue crack expansion modes. The non-proportional additional hardening behavior under different loading paths is closely related to the dislocation substructure. In the rhombic and circular paths, the alloys have higher dislocation density and strong interaction between dislocations and precipitation phases, which is macroscopically expressed as stronger non-proportional hardening ability in the rhombic and circular loading paths.

Experimental study and analysis-oriented model of PET FRP confined ECC cylinders under monotonic axial compression

Recently, several compressive yielding (CY) materials have been developed to improve the flexural ductility of FRP bar-reinforced concrete members, regarding the lack of ductility of FRP bars. However, the currently developed CY materials involving or using steel were not ideal for structures exposed to marine environments. It still needs to develop the non-metal material having CY behavior. This study investigated the failure modes and mechanical properties of large rupture strain (LRS) FRP confined ECC under monotonic axial compression intending to develop it to achieve the demand of CY properties. The results demonstrated that LRS FRP jackets could significantly enhance the compressive ductility (as high as 16.27) of ECC compared to the conventional FRP confined concrete or ECC with the same confinement stiffness of FRP jacket. Moreover, the ductility of LRS FRP confined ECC could reach the ductility of existing CY materials. After developing the dilation model and actively-confined ECC stress–strain model developed based on the database, the analysis-oriented model for LRS FRP confined ECC considering load-path dependence was developed to design the LRS FRP confined ECC as the CY material.

Micro-mechano-morphology-informed continuum damage modeling with intrinsic 2nd gradient (pantographic) grain–grain interactions

In a previous work, we have shown that a granular micromechanics approach can lead to load path dependent continuum models. In the present work, we generalize such a micromechanical approach introducing an intrinsic 2nd gradient energy storage mechanism (resembling pantographic micromechanism), in the grain–grain interaction. Such a mechanism, represents long-range effects but could also be thought as deriving from the utilization of an actual pantographic connection between two grains in a granular metamaterial. Taking advantage of the homogenization approach developed in previous works, we determine the mechanical behavior of the macro-scale continuum and carry out parametric analyses with respect to the averaged intergranular distance and with respect to the stiffness associated to the pantographic term. We show that with the inclusion of the pantographic term mentioned above, the desired thickness of the localization zone can be modeled and finely tuned successfully. We also show that the complex mechanics of load-path dependency can be predicated by the micromechanical effects and the introduced pantographic term.

Ductile failure under non-proportional loading

Ductile failure by void growth in an elasto-plastic material subjected to non-proportional loading, involving step changes in the stress triaxiality or the Lode parameter, is investigated using periodic unit cell model simulations. The equivalent strains to failure by the onset of void coalescence, defined as the localization of plasticity along a band of voids at the micro-scale, are determined as a function of the loading path parameters. The observed trends for the ductility under non-proportional loading are found to be inconsistent with the predictions of a continuum damage mechanics model based on the attainment of a constant critical damage variable, even if the model has been calibrated to predict accurate results for the ductility under proportional loading. It is shown that a recently developed failure criterion based on the onset of plastic instability in a porous material, coupled with a micromechanics-based void growth law, predicts the loading path dependence of failure under non-proportional loading, in better agreement with the cell model simulation results than the continuum damage model. In particular, the triaxiality dependence of the ductility is found to be primarily due to the hydrostatic stress dependence of void growth, while the Lode dependence is primarily due to the instability-based failure criterion with a relatively minor effect of the Lode parameter on void growth. Implications of these findings on the current modeling approaches to ductile failure under shear dominated loading are discussed.

Numerical study of the robustness of steel moment connections under catenary effect

The local fracture will directly result in the consequent decrease in the vertical resistance of the beam-to-column assembly in the steel frame structure, which emphasizes the necessity of the ductile fracture prediction in the numerical study. In this paper, a monotonic plasticity and ductile fracture model is used to characterize the stress state and loading path dependency of the yield surface, as well as the combined effects of the shear stress and hydrostatic pressure on the damage evolution. On the basis of the validated material model, five push-down tests of the beam-to-column assemblies with different moment connections are chosen for the validation of this modeling method in terms of overall vertical force–displacement curves and the local crack initiation and propagation. Thereafter, the numerical studies of the weld access hole reveal that the gentle slope of transition cutting and larger distance between toe of weld access hole and flange weld will raise the connection ductility. The relationship between ultimate chord rotation and these two variables can be formulated by the empirical formulas. As for the bolted web-to-column connection, the deformation capacity can be improved by using compact bolt arrangement and larger bolt size. The implementation of the shear tab with long-slotted holes will also enhance the connection ductility under catenary mechanism. In general, these findings will be benefit to improve the robustness of the steel frame structure, along with the quantitative estimation of connection ductility for checking the structural safety.

Exploring the three-dimensional response of water storage and sewage tunnel based on 3D finite element modeling

Due to the presence of varying inner water head, the mechanical behavior of water storage and sewage tunnel is different from normal transportation tunnels. This paper investigated the three-dimensional response of a staggeredly fabricated water storage and sewage tunnel through sophisticated 3D finite element (FE) modeling, in which detailed configuration of the segmental joints and interactions between different connecting components were reproduced. The FE model and input parameters were validated against precedent full-scale loading testing data under both normal operational and cyclic loading paths considering the periodic variation of inner water head. The characteristics of internal force transmission between longitudinal joints and adjacent segments in the longitudinal direction was investigated, and its spatial variability and loading path dependency were discussed. It is found that this self-adaptive internal force transmission mechanism yields a more compatible loading bearing mode, which is beneficial for deformation control. The influences of some important factors on the three-dimensional response of the lining structure were investigated, including the largest inner water head in loading history, distributions of the longitudinal joints and magnitude of longitudinal thrust force, based on which recommendations for practical design and construction were provided.

Damage and failure mechanisms of ductile metals in biaxial experiments with non‐proportional loading paths

AbstractThe paper deals with an experimental series and corresponding numerical simulations of the biaxial X0‐specimen to study the loading path dependence of ductile damage and fracture under non‐proportional loading. Experimentally the specimen surfaces have been monitored by digital image correlation (DIC). The experimental–numerical technique applied to the non‐proportional biaxial experiments provides new insights of the stress and load‐history dependent damage and fracture processes.

Ductile Fracture Behavior of Mild and High-Tensile Strength Shipbuilding Steels

A comparison is made of the ductility limits of one mild (normal) and two high-tensile strength shipbuilding steels with an emphasis on stress state and loading path dependency. To describe the ductile fracture behavior of the considered steels accurately, an alternative form of ductile fracture prediction model is presented and calibrated. The present fracture model combines the normalized Cockcroft–Latham and maximum shear stress criterion, and is dependent on both stress triaxiality and Lode angle parameter. The calibrations indicate that, depending on the hardening characteristics of the steels, ductile fracture behavior differs considerably with stress state. It is demonstrated that the adopted fracture model is able to predict the ductile fracture initiation in various test specimens with good accuracy and is flexible in addressing the observed differences in the ductile fracture behavior of the considered steel grades.

Unloading behaviors of the rare-earth magnesium alloy ZE10 sheet

Due to their low symmetry in crystal structure, low elastic modulus (∼45 GPa) and low yielding stress, magnesium (Mg) alloys exhibit strong inelastic behaviors during unloading. As more and more Mg alloys are developed, their unloading behaviors were less investigated, especially for rare-earth (RE) Mg alloys. In the current work, the unloading behaviors of the RE Mg alloy ZE10 sheet is carefully studied by both mechanical tests and crystal plasticity modeling. In terms of the stress–strain curves, the inelastic strain, the chord modulus, and the active deformation mechanisms, the substantial anisotropy and the loading path dependency of the unloading behaviors of ZE10 sheets are characterized. The inelastic strains are generally larger under compressive Loading–UnLoading (L–UL) than under tensile L–UL, along the transverse direction (TD) than along the rolling direction (RD) under tensile L–UL, and along RD than along TD under compressive L–UL. The basal slip, twinning and de-twinning are found to be responsible for the unloading behaviors of ZE10 sheets.

Void growth dependence on loading path and mean stress from large-scale numerical simulations

Direct numerical simulation of a large population of voids nucleated from randomly distributed spherical particles is used to assess the load path and mean stress dependence of void growth. The voids are formed by particle failure, and they grow by expansion of the void surfaces through the arbitrary Lagrange/Eulerian mesh. Boundary conditions simulating uniaxial extension and simple shear with varying levels of imposed volume strain provide a range of stress triaxialities and distinct load paths. Volume averages of the void fraction and the mean and effective stresses are extracted from the simulation as measures of the state and loading during dilatational plastic flow.Comparison of the numerical results with the Gurson model shows that the mean stress dependence on the volume fraction follows the Gurson model relatively well at high stress triaxialities but deviates substantially at low triaxialities. Conversely, the effective stress from the Gurson model agrees with the numerical results reasonably well at low stress triaxiality but it deviates appreciably at high stress triaxialities. The results from the simple shear loading are in closer agreement with the Gurson model than the extension results, suggesting load path dependence.

Cyclic Behavior of Wendelstein 7-X Magnet System During First Two Phases of Operation

The sophisticated large magnet system of the Wendelstein 7-X (W7-X) stellarator has been operated during first two experimental campaigns at the Max-Planck-Institute for Plasma Physics in Greifswald, Germany, for roughly 13 months. Its 70 superconducting coils (NbTi CCIC) are extraordinary not only due to complex 3D shapes of 50 non-planar coils, but also due to a non-linear support system. In addition, five big resistive coils with the aim to correct W7-X error fields are installed on the outer cryostat and use rubber pads in their supports to compensate thermal expansion of the coils. The structural behavior of the W7-X magnetic system is monitored and evaluated on the basis of the analysis of the signals from the extended set of mechanical and temperature sensors. Several cooldown/warming up and thousands of electromagnetic cycles with different loading patterns and with up to 70% design load magnitude have been performed by the system successfully. The focus of this paper is on the cyclic structural behavior of the W7-X magnet system and the comparison with finite element predictions. Several related issues such as bolts and rubber pads prestress degradation, support slippage development, evolution of mutual coil displacement, loading path dependence of stress levels, sliding weight support (cryoleg) adjustment, and sensor failure are addressed. Lessons learned so far are also briefly summarized.

Dynamic compression behaviors of concrete under true triaxial confinement: An experimental technique

A dynamic testing system for concrete-like material under static triaxial confinements is developed in the present article. The cubic specimen with length 50 mm is constrained by six steel square bars. The static triaxial confinements are applied on the specimen through six steel bars that independently servo-controlled by three hydraulic cylinders. A striker is then launched to impact the incident bar along the x-axis. The dynamic responses of the cubic specimen are measured by strain gauges stuck on the middle surfaces of the six bars. The dynamic compressive behaviors of concrete specimens under various static triaxial confinements are investigated accordingly. The 3-D dynamic engineering stress- engineering strain relationship, the dynamic volumetric strain- hydrostatic pressure relationship, and the equivalent stress- equivalent strain relationship are obtained and analyzed in details. The results show evidently the load path dependence and the strain rate dependence. Based on the Drucker-Prager (D-P) strength criterion, the effect of the intermediate stress on dynamic strength is discussed, and the material parameters (e.g. α0 and k0) and the strength parameters (e.g. the cohesion c and the inner friction angle ϕ) at various strain rates are demonstrated. The results show that with increasing strain rate, the friction angle ϕ increases, and the cohesion c decreases. The technique provides profound and comprehensive understanding of the dynamic failure properties for concrete-like material under complex stress states.

Compressive strength prediction of fibre reinforced polymer composites under lateral disturbance

Abstract A study on lateral disturbance, which is regarded as a factor that causes imperfect loading, is presented herein. The rationale behind the study is that fiber misalignment has always been regarded as the cause of an imperfect structure. The main purpose of this paper is to establish that even for a perfect structure, lateral disturbance can cause compression instability in a composite. In this paper, a novel numerical model has been established, in which the lateral disturbance effect is applied to a long fiber with perfect alignment to study the compressive instability behavior. The numerical results show that even in the case of perfect structure, lateral disturbance is still the key factor that causes compressive bucking of a composite. In our experiments, the lateral disturbance is observed in-suit from the deformation of the unidirectional (UD) composite using the digital image correction (DIC) technology. Finally, a theoretical prediction model of the compressive strength of fibre reinforced polymers (FRPs) and the effects of lateral disturbance and loading path dependency on compressive behavior of the FRP are also discussed. These results can provide a more comprehensive understanding for the instability mechanism and the compressive strength of FRPs composite.

Micromechanical modeling and simulation of the loading path dependence of ductile failure by void growth to coalescence

The loading path dependence of ductile failure by void growth to coalescence is studied using a unit cell model of a porous material, containing a periodic distribution of voids in an elasto-plastic power law hardening matrix. The unit cell is subjected to triaxial proportional loading paths, and predictions for the strains to failure, defined as the onset of void coalescence by plastic strain localization in the inter-void ligaments, are obtained as a function of the loading path parameters, the stress triaxiality and the Lode parameter. Analogous simulations of a macroscopic material element subjected to proportional loading are performed using a multi-surface plasticity model, which accounts for void growth by diffuse plastic flow and void coalescence by the localization of plastic strains inside a micro-scale representative volume element. A phenomenological hardening law that approximately accounts for the physics of strain hardening during both pre- and post-coalescence deformation is proposed. The strains to failure in the continuum simulations are determined as the equivalent strains to the onset of void coalescence at the micro-scale of the voids. It is shown that the multi-surface plasticity model quantitatively predicts the loading path dependence of the strains to failure obtained from the cell model simulations over a wide range of values of the Lode parameter, from axisymmetric to shear dominated states, and moderate to large values of the stress triaxiality. Quantitative agreement with cell model simulations is obtained for two representative values of the strain hardening exponent, and in the absence of heuristic adjustable parameters in the model.

Ductile failure simulations using a multi-surface coupled damage-plasticity model

Ductile failure of isotropic porous materials is studied using a coupled damage-plasticity model, accounting for void growth by diffuse plastic flow as well as void coalescence by plastic flow localization in the inter-void ligaments. The model is based on a multi-surface yield criterion, consisting of the Gurson yield criterion for a porous representative volume element (RVE) undergoing diffuse yielding, and additional yield criteria corresponding to localized yielding of the RVE within discrete coalescence bands whose orientations depend on the applied state of stress. Approximate closed form solutions for the orientations of the potential coalescence bands as a function of the applied stress are obtained; and a closed form expression for the coalescence criterion, expressed in terms of the principal stresses, is proposed. The predicted shapes of the multi-surface yield loci at large values of the porosity have a marked resemblance to the Mohr-Coulomb yield locus for granular materials on octahedral section planes, and reduce approximately to the Gurson yield locus for small values of the porosity. The plasticity model is integrated numerically under proportional loading conditions, and predictions for the strains to failure are obtained as a function of the loading path parameters, the stress triaxiality and the Lode parameter. The predicted trends for the loading path dependence of ductility are shown to be in good qualitative agreement with the results of recent micromechanical voided cell simulations under combined tension and shear. Finally, predictions for the strains to failure in smooth and notched bar tension experiments are obtained from finite element simulations using the multi-surface and the widely used Gurson-Tvergaard-Needleman (GTN) models. It is shown that the multi-surface model, in the absence of heuristic adjustable parameters, quantitatively predicts similar values of the overall strains to failure as the GTN model; using typical values of the parameters in the latter model.

Experiments with the X0-specimen on the effect of non-proportional loading paths on damage and fracture mechanisms in aluminum alloys

The paper deals with an experimental series with the new biaxial cruciform X0-specimen to study the stress state and loading path dependence of ductile damage and fracture. The ongoing material deterioration is studied experimentally to develop and validate corresponding phenomenological damage and fracture models.In this context the new cruciform X0-specimen has been proposed which is characterized by four independent notched regions where inelastic deformations as well as damage and fracture are localized. The specimen allows investigation of a wide range of stress states and can be applied for different loading paths. A series of biaxial experiments with proportional and corresponding non-proportional loading paths has been performed and the experimental technique with different loading histories is presented in detail. The experiments have been monitored by a special six camera DIC setting allowing even the analysis of the specimen behavior in thickness direction. Furthermore, the fracture surfaces have been analyzed by scanning electron microscopy (SEM). The results based on proportional and non-proportional loading paths clearly show that damage and fracture processes are load-path-dependent.