Effect Of Loading Path Research Articles

On Dimensional Control in Rotary Stretch Bending of Aluminum Profiles: Loading-Path Effects

In this research, the influences of loading paths on dimensional accuracy in a newly developed flexible rotary stretch bending process were investigated by experimental and numerical approaches. A series of carefully controlled bending experiments were conducted using AA6082-T4 rectangular, hollow profiles. Several representative loading paths — including (i) kinematically-controlled simultaneous stretching and bending; (ii) pre-stretching prior to bending; (iii) post-stretching subsequent to bending; (iv) pre-stretching prior to and post-stretching subsequent to bending — were designed and tested for a given geometrical configuration of bent parts. The critical dimensional characteristics, such as global shape (elastic springback) and cross-sectional deformation, were analyzed and discussed for the products formed under the above-designed loading paths (i)-(iv). Furthermore, finite element analysis was conducted to gain additional insights into the deformation mechanisms that take place for various loading paths. Finally, a guideline for designing the loading paths was developed, thus providing improved process control for achieving formed products with high dimensional accuracy.

Progressive damage and failure analysis of three-dimensional braided composites under multiaxial loadings

A meso-mechanical computational model based on the finite element method (FEM) is developed to predict the progressive elastic-plastic damage and failure behavior of three-dimensional four directional (3D4D) braided composites under multiaxial loadings. Firstly, the constitutive laws for mesoscale constituents (i.e. yarn, matrix and interface) of braided representative volume element (RVE) are established and implemented by the user defined material subroutine UMAT in ABAQUS. Then, how to build the braided RVE and conduct the simulation are introduced. After that, the uniaxial tensile data is used to verify the proposed model. Finally, the damage and failure behavior of the RVE under multiaxial loadings is investigated, considering the effects of loading paths and interface. The results show that loading path and interface have little effect on the strengths. The predicted failure envelopes in different stress spaces for RVE are compared with the Tsai-Wu and Hoffman theories, which are much closer to the Tsai-Wu theory.

Rate-dependent multiaxial life prediction for polyamide-6 considering ratchetting: Semi-empirical and physics-informed machine learning models

The rate-dependent multiaxial fatigue life of PA6 is investigated by conducting a series of stress-controlled multiaxial fatigue tests involving the ratchetting. Based on the obtained experimental results and the critical plane approach, a semi-empirical life-prediction model is proposed, in which the effects of loading path, stress level, and stress rate are considered. To avoid the simplifications included in the semi-empirical model, a hybrid life-prediction model combing the critical plane approach and neural network is further developed for obtaining better accuracy and applicability. In addition, to compensate the insufficiency of data samples, two physical constraints (i.e., restricting the space of model parameters and generating domain knowledge-based data samples) are designed. The results demonstrate that: the hybrid model presents a better prediction accuracy than that of semi-empirical one; furthermore, by embedding the designed constraints into the hybrid model to steer the training of NN, the physically consistent solution is obtained and the extrapolation performance of modified hybrid model is significantly improved.

Multiaxial fatigue life prediction for metallic materials considering loading path and additional hardening effect

PurposeA large number of data have proved that under the same von Mises equivalent strain condition, the fatigue life under multiaxial non-proportional loading is often much lower than the life under multiaxial proportional loading. This is mainly due to the influence of the non-proportional loading path and the additional hardening effect, which lead to a sharp decrease in life.Design/methodology/approachThe modulus attenuation effect is used to modify the static hardening coefficient, and the predicted value obtained is closer to the additional hardening coefficient obtained from the experiment. A fatigue life model can consider non-proportional paths, and additional hardening effects are proposed. And the model uses multiaxial fatigue test data to verify the validity and adaptability of the new model. The life prediction accuracy and material application range are satisfactory.FindingsBecause loading path and additional hardening of the material affect fatigue life, a new multiaxis fatigue life model based on the critical plane approach is proposed. And introducing a non-proportional additional damage coefficient, the joint influence of the load path and the additional hardening can be considered. The model's life prediction accuracy and material applicability were verified with multiaxial fatigue test data of eight materials and nine loads compared with the prediction accuracy of the Kandil–Brown–Miller (KBM) model and Fatemi–Socie (FS) model.Originality/valueThe physical meaning of the new model is clear, convenient for practical engineering applications.

A true triaxial experimental study on porous Vosges sandstone: from strain localization precursors to failure using full-field measurements

This study systematically investigates the effect of deviatoric loading paths on diffuse and localized deformation developing during the mechanical loading of a high porosity (20%) Vosges sandstone (Eastern France). Laboratory scale experiments are performed using a high pressure true triaxial apparatus, designed to provide access to full-field surface kinematics at high spatial and temporal resolutions during the loading phase. The true triaxial experiments, with independent control of the three principal stress, are conducted at two constant mean stresses, in the brittle-ductile transition regime, and at five prescribed Lode angles , from axisymmetric compression (ASC) to axisymmetric extension (ASE). First, the transition from diffuse towards localized deformation is analyzed in different loading increments and shows an intermediate step of early strain localization , characterized by a large number of early deformation bands developing well before the stress peak and with a predominantly dilatant behavior. Secondly, the evolution of the mechanical behavior and localization patterns, such as deformation band angles and localized dilatancy , indicate a transition from the brittle regime to the ductile regime that is not only dependent on an increase in the mean stress, but also on a decrease in the Lode angle. The analysis of full-field measurements also provides insights into the emergence and evolution of local strains, as deformation structures coalesce or relocate and different failure modes develop depending on the prescribed stress paths.

Analytical study on the composite behavior of rectangular CFST columns under combined compression and torsion

In this paper, a total of 44 rectangular CFST column finite element models are established and verified. The effect of loading path, the working mechanism and the constraint interaction of rectangular CFST column under compression-torsion loading are discussed. The obtained results show that the ultimate axial bearing capacity of CFST column is decreased when the torsional moment is applied first, and the ultimate torsional capacity is increased when the compression force is applied first. The working mechanism of the compression-torsion CFST column can be simplified as unity of “pulling/compressive torsion” of the steel tube and “compressive torsion” of the core concrete. Finally, the torque-axial force correlative formula of rectangular CFST column is proposed, and is verified well with the test results and finite element results with higher accuracy and less dispersion.

Buckling of thick elasto-visco-plastic egg shells under external pressure: Experiments and bifurcation analysis

The buckling of rate dependent structures is not a topic often discussed in the literature. Methods to predict the buckling of such structures exist, but only few experimental works have been published, and even less when considering thick shell structures. In this work we are interested in the buckling of thick elasto-visco-plastic hemi-egg shells. We follow a modelling/experimental approach to analyse such problem. Buckling experiments at room temperature on hemi-egg shells subjected to external pressure are performed. 3D digital image correlation is used to measure the displacement fields on the inner surface of the hemi-egg shell during the buckling experiments. Due to the specimen shape and their loading, they experience non-proportional load paths. The effect of a non-proportional load path on the buckling behaviour has already been discussed many times in the literature for elasto-plastic materials. This work also intends to assess this point for a rate dependent material. A buckling prediction model is used to predict the buckling of hemi-egg shells. This model couples Bodner’s approach with the deformation theory. It is used to estimate the buckling critical times and the buckling modes based on a preliminary finite element analysis. The effects of geometrical and loading imperfections on the buckling behaviour of the hemi-egg shells are also discussed. Finally, the experimental results are compared to the buckling predictions. A good correlation is observed between numerical results and experiments.

Deep learning based phase transformation model for the prediction of microstructure and mechanical properties of hot-stamped parts

Hot stamping of boron steel is an effective way for weight reduction of automobiles parts, but suffers from the loss of mechanical properties due to incomplete martensitic transformation. Different from general heat treatment, phase transformation in hot stamping relates to both thermal loading path and deformation history. Unfortunately, the existing models have difficulty in capturing the history-dependent phase transformation behavior of boron steel under hot stamping conditions. In the present work, the gated recurrent unit (GRU) are combined with fully connected neural network (FCNN) to capture the coupling effect of both nonlinear strain history and thermal loading path on phase transformation. A unified deep-learning based phase transformation (DLPT) model is developed to integrate both diffusive and diffusionless transformation to cover all feasible thermo-mechanical loading path in hot stamping process. A hybrid driven thermo-mechanical-metallurgical (TMM) framework is developed by integrating the DLPT model into general TMM framework, which providing a novel approach for two-scale simulation of hot stamping process. A comprehensive database of phase transformation is constructed for model training based on well-designed thermo-mechanical loading experiments to cover hot stamping conditions, and the optimal topology of neural network in DLPT model is obtained by training on this database. The accuracy and reliability of DLPT model is systematically demonstrated by dieless hot V-bending and hot stamping of T-shaped parts besides CCT and DCCT tests. The net effect of local plastic strain on subsequent phase transformation is clarified with accuracy by dieless V-bending with the removal of disturbing factors. Non-uniform distribution in hardness of the final hot stamped parts can be predicted with the DLPT model successfully, which is better in accuracy than in case of working with the conventional model.

Effect of loading path on grain misorientation and geometrically necessary dislocation density in polycrystalline aluminum under reciprocating shear

Solid phase processing (SPP) is a promising alloy fabrication technique to produce fine and homogeneous grain structures for high-performance alloys. However, there is very limited modeling capability to understand and predict the grain refinement during SPP. In this work, the crystal plasticity theory was used to study elastic–plastic deformation in polycrystalline aluminums under large shear deformation. Two approaches, kernel averaged misorientation (KAM) and grain reference orientation deviation (GROD), were used to assess the grain misorientations. The geometrically necessary dislocation (GND) density was computed with the plastic strain rate. The deformation simulations were carried out under two loading conditions to investigate the effect of loading paths on the evolutions of grain misorientation and GND density. The results show that the regions with high misorientation and GND density first appear near grain boundaries. These regions then extend toward interior grains. The loading path affects plastic deformation accumulation and recovery, hence dislocation evolution and misorientation. Both two- and three-dimensional simulations showed that the spatial and temporal evolutions of GROD, KAM, and GND density are closely correlated, which indicates they all can be used as criteria of grain refinement or recrystallization, the essential information for grain refinement simulations.

An Experimental Investigation of the Gas Permeability of Tectonic Coal Mineral under Triaxial Loading Conditions

Underground coal mining of CH4 gas-rich tectonic coal seams often induces methane outburst disasters. Investigating gas permeability evolution in pores of the tectonic coal is vital to understanding the mechanism of gas outburst disasters. In this study, the triaxial loading–unloading stresses induced gas permeability evolutions in the briquette tectonic coal samples, which were studied by employing the triaxial-loading–gas-seepage test system. Specifically, effects of loading paths and initial gas pressures on the gas permeability of coal samples were analyzed. The results showed the following: (1) The gas permeability evolution of coal samples was correlated with the volumetric strain change during triaxial compression scenarios. In the initial compaction and elastic deformation stages, pores and cracks in the coal were compacted, resulting in a reduction in gas permeability in the coal body. However, after the yield stage, the gas permeability could be enhanced due to sample failure. (2) The gas permeability of the tectonic coal decreased as a negative exponential function with the increase in initial gas pressure, in which the permeability was decreased by 67.32% as the initial gas pressure increased from 0.3 MPa to 1.5 MPa. (3) Coal samples underwent a period of strain development before they began to fail during confining pressure releasing. After the stress releasing-induced yield stage, the coal sample was deformed and cracked, resulting in a quickly increase in gas permeability. With a further releasing process, failure of the sample occurred, and thus induced rapidly increasing gas permeability. These obtained results could provide foundations for gas outburst prevention in mining gas-rich tectonic coal seams.

Effect of unidirectional lateral cyclic load path on hysteretic response of battened steel columns – A numerical investigation

During earthquakes, battened steel columns are subjected to both compressive load in longitudinal direction and cyclic load in lateral direction. The effects of unidirectional lateral cyclic stress on a double channel battened column (DCC) were investigated using ABAQUS software in this paper. Four different unidirectional lateral displacement controlled load paths (U1, U2, U3, and U5) were considered for this study. As per the study, the lateral load carrying capacity (LCC) and peak lateral displacement are significantly affected by the unidirectional lateral cyclic loading path. The results showed that the peak lateral displacement of the columns reduces considerably, with a minor effect on LCC when number of cycles applied for certain deformation level increases.

Numerical analysis of damage and fracture in steel sheets undergoing non-proportional loading paths

The paper deals with the numerical analysis of damage and fracture mechanisms in steel sheets. Newly developed H-specimens are taken from thin sheets and are tested under different biaxial loading conditions. Results of numerical simulations of a series of biaxial experiments are presented showing also the effect of non-proportional loading paths on inelastic deformation behavior and on damage processes. In this context, an anisotropic continuum damage model is presented based on yield and damage conditions as well as evolution laws for plastic and damage strain rates. Different stress-state-dependent branches of the damage criteria are taken into account corresponding to various damage and failure processes on the micro-scale depending on the stress triaxiality and the Lode parameter. Experiments with the biaxially loaded H-specimen have been performed. Results for proportional and corresponding non-proportional loading histories are discussed. During the experiments strain fields in critical regions of the specimens are analyzed by digital image correlation (DIC) technique. Numerical simulations of the experiments have been performed and numerical results are compared with experimental data. Furthermore, based on the numerical analysis evolution of stress variables is examined and stress distributions in critical specimens areas are detected allowing prediction of stress-state-dependent damage and fracture mechanisms. The numerical results also demonstrate the efficiency of the experimental program and the new specimens geometries covering stress states in the shear-tension regime as well as the effect of the loading histories on inelastic deformation and damage behavior in steel sheets.

Evaluation of multiaxial fatigue life prediction approach for adhesively bonded hollow cylinder butt-joints

The low-cycle fatigue experiments of the adhesively bonded hollow cylinder butt-joints were conducted in previous work. The effects of loading path, stress amplitude, mean stress and cycle time on the fatigue life were discussed briefly. The stress-based and energy-based fatigue life prediction models were developed to predict the fatigue life of the adhesively bonded joints, respectively. The effects of loading paths and loading conditions on the fatigue life were considered in the prediction models. The prediction results demonstrated that the stress-based model presented a good prediction by reasonably selecting the loading path coefficients and model constants. Furthermore, the energy-based fatigue life prediction model also achieved an accurate prediction on the multiaxial fatigue life through considering the dissipation energy as fatigue failure parameter. In addition, the neural network based method was adopted to predict the multiaxial fatigue life of the adhesively bonded joints. It was shown that the neural network based method obtained a more accurate prediction for the multiaxial fatigue life of the adhesively bonded joints compared with the previous two prediction models. Moreover, the evaluation of the applicability and accuracy of these three prediction methods was carried out. It indicated that the neural network based method had the simple prediction process and it was more accurate than that of the two models for the multiaxial fatigue life prediction of adhesively bonded joints.

Damage and quantitative indexes for steel reinforced concrete column with T-shaped section

This paper presents an experimental investigation on damage performance of nine steel reinforced concrete (SRC) columns with T-shaped section under different loading paths. The monotonic loading, low cyclic reversed loading and mixed loading were applied to specimens along the flange of specimen. Furthermore, different axial compression ratios and steel ratios were used to study the damage of specimen. The failure modes were observed and the load-displacement curves were analyzed. The results indicate that the specimens mainly showed the feature of bending failure accompanied by bond failure characteristic at the end of loading. The load-displacement curve was plump and symmetrical without obvious pinch under the low cyclic reversed loading. The ductility coefficient lied within the range of 5.34–9.41, which indicates that these columns had better deformation capability. Based on the experimental results, a modified damage model considering deformation and energy dissipation was proposed, where the effects of concrete cracking, loading path and effective energy dissipation on damage were studied. Moreover, the damage index at each loading stage was calculated. Meanwhile, the level of seismic performance of SRC T-shaped column was divided into five levels, namely the normal use, the basic normal use, the temporary use, the post-repair use, and the near serious damage. Many SRC T-shaped columns were chosen as the analysis samples to obtain the displacement angles under different loading stages. Based on statistic results, the corresponding relationship between quantitative index of displacement angle and the damage index was established.

Compaction of the Groningen Gas Reservoir Sandstone: Discrete Element Modeling Using Microphysically Based Grain‐Scale Interaction Laws

AbstractReservoir compaction, surface subsidence, and induced seismicity are often associated with prolonged hydrocarbon production. Recent experiments conducted on the Groningen gas field's Slochteren sandstone reservoir rock, at in‐situ conditions, have shown that compaction involves both poroelastic strain and time independent, permanent strain, caused by consolidation and shear of clay films coating the sandstone grains, with grain failure occurring at higher stresses. To model compaction of the reservoir in space and time, numerical approaches, such as the Discrete Element Method (DEM), populated with realistic grain‐scale mechanisms are needed. We developed a new particle‐interaction law (contact model) for classic DEM to explicitly account for the experimentally observed mechanisms of nonlinear elasticity, intergranular clay film deformation, and grain breakage. It was calibrated against both hydrostatic and conventional triaxial compression experiments and validated against an independent set of pore pressure depletion experiments conducted under uniaxial strain conditions, using a range of sample porosities, grain size distributions, and clay contents. The model obtained was used to predict compaction of the Groningen reservoir. These results were compared with field measurements of in‐situ compaction and matched favorably, within field measurement uncertainties. The new model allows systematic investigation of the effects of mineralogy, microstructure, boundary conditions, and loading path on compaction behavior of the reservoir. It also offers a means of generating a data bank suitable for developing generalized constitutive models and for predicting reservoir response to different scenarios of gas extraction, or of fluid injection for stabilization or storage purposes.

Local Buckling Characteristics of Stainless-Steel Polypropylene Deep-Sea Sandwich Pipe under Axial Tension and External Pressure

In this paper, the effects of different loading paths of axial tension and external pressure on the collapse pressure of sandwich tubes are studied by experiments and finite element models. The difference of the two loading paths is investigated. Eight experiments were carried out to study the influence of different loading paths on pipeline collapse pressure under the same geometric and material parameters. Parameterization studies have been carried out, and the results are in good agreement with the experimental results. The test and finite element results show that the loading path of external pressure first and then the axial tension (P→T) is more dangerous; the collapse pressure of the sandwich pipe is smaller than the other. Through parametric analysis, the influence of the axial tension and the diameter-to-thickness ratio of the inner and outer pipe on the collapse pressure under different loading paths are studied.

Creep–fatigue life evaluation of type 304 stainless steel under non-proportional loading

The fatigue life of stainless steel under multiaxial loading conditions as a consequence of multiple damage effect occurring at elevated temperature is a topic of great importance. However, the interaction of creep, fatigue, and multiaxial non-proportional loading is poorly understood owing of a lack of experimental data obtained under multiaxial loading conditions. In the present study, data of previous creep–fatigue experiments performed on type 304 stainless steel under multiaxial loading conditions are summarized from available literature. These test results include the effects of strain rate, asymmetric strain waveform, and loading path on the creep–fatigue life of the stainless steel. Then, additional creep–fatigue tests are performed on the stainless steel under non-proportional loading conditions with four strain rates at 873 K in air. The applicability and limitations of several frequency-based life prediction models are discussed on the basis of the experimental results. Finally, an improved version of the frequency modified damage function (FMDF) model considering the effects of various loading path is proposed. The new model shows good correlation with the failure lives under multiaxial proportional and non-proportional loading conditions at elevated temperatures.

Effect of seat-type abutment load path and failure mode on seismic response of straight ordinary bridges

The simplified modeling and analysis procedures commonly used in the design and assessment of bridges utilize one-dimensional (1D) spine elements and springs. These procedures have been well vetted for columns and some capacity-protected members, such as the girders. However, the abutment also contributes to the lateral load resisting system, and the simplified models may not capture the actual load path, failure modes, or dynamic response of either the bridge system or the abutment itself. This paper identifies through static three-dimensional continuum modeling the load path, component contributions to subsystem resistance, and failure modes that should be used in simplified modeling approaches of seat-type abutments. The consequences of common modeling assumptions and simplifications on bridge design and assessment were determined by comparison with 1D simplified models. It was found that the use of modeling simplification substantially underestimates the subsystem resistance. The effect of abutment characteristics, including stiffness and strength in the longitudinal and transverse directions, on nonlinear dynamic bridge seismic demand prediction were investigated with reduced order dynamic models. The increase in abutment stiffness and strength reduces the bridge system’s displacements and increase forces significantly.

A new microstructure‐based multiaxial fatigue life prediction model for A319 casting alloys

AbstractThis paper describes a microstructure‐based multiaxial nonproportional fatigue life prediction model applied to A319 alloy. The materials made with different casting cooling rates and Sr modification are characterized and quantified in terms of secondary dendrite arm spacing, size, and aspect ratio of eutectic Si particles. Multiaxial nonproportional fatigue tests have been performed on six groups of A319 alloys to systematically analyze the effect of microstructure and loading path on the fatigue properties of Al–Si cast alloy. The first part of the paper is focused on microstructure quantitative characterization to determine the influence of different casting conditions, followed by stress response behavior and fatigue fracture analysis. Finally, a new multiaxial fatigue life prediction model for Al–Si alloy is proposed, for which 56% of the data points fall in the bound lines of factor of 2 and 83% of the data points fall in the bound lines of factor of 3.

The effects of loading path on process parameters in the free tube forming process

The free bending method is the simplest method among the tube bending processes without the use of a die. Despite the simplicity of the process, there is no proper control over the geometrical tolerance of the product. The loading path or in other words the bearing movement mechanism is one of the effective factors on product geometry. In this paper, a finite element simulation has been carried out to investigate two different bearing movement time-paths (synchronous and asynchronous mechanisms); then, the results have been verified with experimental tests. The thickness distribution in different directions, ovality, bending radius, and applied forces on the bearing and the tube for both bearing movement mechanisms are the main results of this paper. The amplitude of thickness change in both mechanisms was equal. But there is a uniform trend in variation of thickness distribution in synchronous mechanisms. So, better geometrical quality of products is expected in this mechanism. On the other hand, because of uniform force distribution with tube movement in the bearing and tube, the stability of the asynchronous mechanism is higher than the synchronous mechanism.