Effect Of Loading Path Research Articles

Ductile fracture of aluminum 2024-T351 under proportional and non-proportional multi-axial loading: Bao–Wierzbicki results revisited

The effect of stress state and loading path on the ductile fracture of aluminum 2024-T351 is characterized through tension–torsion experiments on tubular specimens. The experimental program includes proportional and non-proportional loading paths leading to the onset of fracture at nearly plane stress conditions at stress triaxialities between 0 and 0.6. Stereo digital image correlation is used to measure the displacements and rotations applied to the specimen shoulders. An isotropic non-quadratic Hosford plasticity model with combined Voce–Swift hardening is used to obtain estimates of the local stress and strain fields within the specimen gage section. The hybrid experimental–numerical results indicate a higher strain to fracture for pure shear than for uniaxial tension. The calibration of a Hosford–Coulomb fracture initiation model suggests that the ductility of aluminum 2024-T351 decreases monotonically as a function of the stress triaxiality, whereas it is a non-symmetric convex function of the Lode angle parameter. It is shown that a simple non-linear damage accumulation rule can describe the effect of non-proportional loading on the strain to fracture.

On the force–displacement law of contacts between spheres pressed to high relative densities

A finite element study of the interparticle force–displacement laws on contacts of spheres at conditions corresponding to compacts pressed to high relative densities is presented here. Under these conditions, the response of a contact can be affected by the presence of neighboring contacts. Finite element simulations of axisymmetric models of equispaced and equally loaded contacts show that the force–displacement law is not unique and depends on the number of neighboring contacts. The force at a given interparticle deformation is minimum for Z=2 but at higher coordination numbers becomes larger after a critical deformation due to the interaction of the stress fields of neighboring contacts. This difference is magnified when the local porosity closes. Furthermore, numerical simulations of periodic arrays of spheres were conducted to assess the effect of loading path and the formation of new contacts on the response of existing contacts. In both cases, it was found that, the contact response depends on the overall triaxiality of the deformation of the particle. A new deformation fabric tensor is proposed based on the deformation and direction of all contacts on a particle. The first and second invariants of this tensor are used to characterize the triaxiality of the deformation on a particle. These results form the basis for more appropriate force–displacement laws at contacts that can be implemented in discrete element simulations for high density problems.

Minimum Circumscribed Ellipse (MCE) and Stress Scale Factor (SSF) criteria for multiaxial fatigue life assessment

Many fatigue models proposed in literature are validated by the author’s data and usually they are not corroborated with other author’s lab work. In this paper, two multiaxial fatigue criteria, the Minimum Circumscribed Ellipse (MCE) and the Stress Scale Factor (SSF), are used to assess fatigue life under multiaxial loading conditions. Two different sets of fatigue data obtained from two different steels and from two different research groups were used in order to evaluate the accuracy of the models MCE and SSF regarding multiaxial fatigue life assessment. The fatigue data used here have two major features: stress concentrations, always present in mechanical components, and the loading path effects, with the inherent changing on the principal stress directions and/or the variation of the stress amplitude ratio (tau/sigma). Furthermore, different failure criteria were adopted for each material and different testing setup. For the Ck45 material, the failure criterion was the crack initiation, for the C40 material was the total rupture. Another factor to point out is that the Ck45 fatigue results were obtained under bending/torsion conditions and the C40 fatigue results were achieved in axial/torsion loading conditions. Results show good correlation between experiments and fatigue life estimations. Some remarks and conclusions concerning the performance of the MCE and SSF models are presented.

A new finite element approach for modelling ductile damage void nucleation and growth—analysis of loading path effect on damage mechanisms

A two-dimensional finite element (FE) model is presented to model the nucleation and void growth stages in ductile damage phenomena on the microstructure scale. This model is based on a level-set (LS) method coupled with an advanced re-meshing strategy. Both nucleation modes (interface debonding and inclusion fracture) are modelled through the introduction of micro-voids according to stress-based criteria. The LS method and mesh adaptation are used to accommodate the topology modification of the microstructure and to model multiple void nucleation and growth for different loading paths. The enhanced FE model is adopted to analyse the key features of the damage mechanisms on the micro-scale. The effects of inclusion orientation and of a complex loading path on nucleation and void growth are addressed. Good agreement is found with available experimental and numerical data found in the literature. The results exhibit that the loading path is a key point in damage growth. The proposed FE framework is an efficient technique to study damage phenomena on both simple and realistic microstructures. In the future, such an approach can be used to calibrate macroscopic ductile damage models for a complex loading path.

Prediction of Cyclic Residual Stress Relaxation by Modeling Approach

A new method for prediction of residual stress cyclic relaxation has been developed and implemented in the finite element software Abaqus. The calculated profiles were validated by experimental measurements using X-ray diffraction method. This validated approach is afterward used to investigate the effect of loading path and initial residual stress characteristics on the kinetics of relaxation and the stabilized profile for both cyclic softening and cyclic hardening materials.

Analysis of the effect of the loading path on the failure behaviour of slopes

The effect of the loading path on the failure behaviour of slopes was investigated based on the centrifuge model test observations under the application of two typical loading paths: self-weight loading by increasing the centrifugal acceleration and excavation at a constant centrifugal acceleration. Compared with the self-weight loading condition, the slope was more likely to fail under excavation condition, with a significantly deeper slip surface. The quantification results showed that the sequences of slip surface formation associated with the two types of loading path proceeded in opposite directions. A reasonable stability analysis method of slopes should consider the progressive failure and the effect of loading path.

Experimental and numerical analysis about the cyclic behavior of the 304L and 316L stainless steels at 350 °C

In a previous study, we have demonstrated that cyclic accumulation of the inelastic strain exhibited by 304L SS at room temperature under tension–compression stress control is mostly due to creep (Taleb and Cailletaud, 2011). The same result in the same conditions is pointed out for 316L SS (Taleb, 2013a). In the present paper, the cyclic behavior of both 304L and 316L stainless steels at 350°C is investigated. Creep is not significant at this temperature. In addition to tension–compression tests, the effect of non-proportional loading paths (axial-torsion) is considered for both stress and strain controlled conditions. The study suggests that ratcheting is very small with the different mean stress and amplitude used remaining into the assumption of small strains; this observation may be linked to the large cyclic hardening exhibited by both materials. However ratcheting seems more important under non-proportional loading path compared to the equivalent tension–compression conditions. A multi-mechanism model has been used to simulate the whole experimental data base. After the identification process of the material parameters conducted by considering only strain controlled experiments, its predictive capabilities have been evaluated on the stress controlled tests. The model presents a very good quantitative agreement with the quasi absence of ratcheting. However, the model fails in describing the over-hardening (mostly isotropic) observed under monotonic loading when the maximum strain is large (about 4%).

The influence of shock-loading path on the spallation response of Ta

Spallation is well known to be a complex process strongly influenced by microstructure, loading path, and the loading profile yet often a singular "spall strength" is utilized in hydrocodes to quantify the dynamic fracture behavior of a material. In the current study, the influence of loading path on the "spall strength" and damage evolution in high-purity Ta is presented. Tantalum samples where shock loaded to three different peak shock stresses using both symmetric impact, and two different composite flyer plate configurations such that upon unloading the three samples displayed nearly identical "pull-back" signals as measured via rear-surface velocimetry. While the "pull-back" signals observed are similar in magnitude, the highest peak stressed sample resulted in complete spall scab separation while the two lower peak stresses resulted in incipient spall. The damage evolution in the "soft" recovered Ta samples was quantified using optical metallography, electron-back-scatter diffraction, and tomography. The effect of loading path on spallation and its ramifications for the stress and kinetic dependency of dynamic damage evolution is discussed.

The Effect of Loading Path on Forming Results in Multi-Gripper Flexible Stretch Forming

Multi-gripper flexible stretch forming (MGFSF) is a recent technological innovation of sheet metal flexible forming process. Straight jaws in traditional stretch forming machine are replaced by a pair of opposed clamping mechanisms which can move relative to each other. Taking the case of forming a sheet metal into spherical surface by stretching the sheet in two opposite directions, the finite element models of MGFSF under various loading paths were established and the effects on stretch amount, strain and thickness of the simulated parts were analyzed comparatively. It is founded that compared to the horizontal-tilting (HT) and horizontal-vertical (HV) loading paths, the horizontal-tilting-vertical (HTV) loading path would result in more uniform stretch amount, strain and thickness distributions also with lower strain and thickness reduction, which improves the forming quality significantly. Finite element simulations also revealed that the material flow state in the transition zone can be improved effectively and the local strain concentration can be greatly suppressed with reasonable loading path, which would decrease the possibility of material failure.

Numerical investigation on the performance of concrete-filled double-skin steel tubular members under tension

This paper presents a numerical investigation on the tensile behaviour of concrete-filled double-skin steel tubular (CFDST) member. A comprehensive finite element (FE) model is established and calibrated against the test results for the CFDST members under concentric and eccentric tension. The comparison shows that the proposed FE model is capable to capture the structural behaviour of the tensile specimens. Parametric studies are then conducted to investigate the influence of some key parameters, such as the material strength, the nominal steel ratio and the hollow ratio on the tensile behaviour of composite members. The steel–concrete composite action, the effect of loading paths and the tension–bending interaction diaphragm are also discussed. It is found that the tensile strength of the member depends on the composite action between steel tubes and sandwich concrete, and the tension–bending interaction diaphragm can be represented by a simple linear relationship. Finally, the design equation to predict the tensile strength of CFDST member is proposed, and the comparison results show that the proposed equation has a good accuracy.

Process Parameter with High Expansion Rate of SUS304 Tube Hydroforming

Stainless steel has been applied more and more extensively because it has good corrosion resistance and its surface is glossy, like a mirror after polishing. Thus, it is used in high-price pieces or quality goods. In this paper, the SUS 304 has been used to form a product with high expansion rate, via tube hydroforming technology, applying different feeding of two ends with different inner pressure to complete the procedure. The effects of different loading paths on product quality are discussed in this paper. Finally, by reasonable feeding with pressure parameters and a preforming process, a product with high expansion rate has been realized. The diameter-to-thickness ratio is 110, with an expansion rate of about 45%. The deviation of results from the experiment and simulation are also discussed in this paper. The results of this study could provide significant information to benefit industry.

Fatigue assessment of friction stir channels

Friction Stir Channelling (FSC) is an innovative process within solid-state manufacturing technologies able to produce continuous internal or open channels in monolithic plates. The high level of adaptability of FSC makes it possible to apply to many different technical field domains and can bring significant advantages for already existent and new industrial applications. Because engineering components and structures are subject to accidental failures that occur due to unexpected or additional loadings, such as additional axial or torsion, this paper is focused on the effects of multiaxial loading paths on fatigue life of friction stir channelling monolithic plates of AA5083-H111 aluminium alloy.Uniaxial and biaxial fatigue tests were carried out with a stress ratio of R=−1. The FSC specimens used in this study were specially designed for the purpose. The fatigue behaviour was investigated by load controlled tests under uniaxial tension/compression loading and combined axial and torsional proportional loading. Metallographic analysis of the channel microstructure and fractograph analysis of the fracture surfaces were performed by optical microscope and SEM, respectively. For all tests carried out, the first crack always has initiated at the top of the advancing side namely in the boundary between the nugget and the thermo-mechanically affected zone.

Micromechanical study of the loading path effect in high cycle fatigue

In this work, an analysis of both the mechanical response at the grain scale and high cycle multiaxial fatigue criteria is undertaken using finite element (FE) simulations of polycrystalline aggregates. The metallic material chosen for investigation, a pure copper, has a Face Centred Cubic (FCC) crystalline structure. Two-dimensional polycrystalline aggregates, which are composed of 300 randomly orientated equiaxed grains, are loaded at the median fatigue strength defined at 107cycles. In order to analyse the effect of the loading path on the local mechanical response, combined tension–torsion and biaxial tension loading cases, in-phase and out-of-phase, with different biaxiality ratios, are applied to each polycrystalline aggregate. Three different material constitutive models assigned to the grains are investigated: isotropic elasticity, cubic elasticity and crystal plasticity in addition to the cubic elasticity. First, some aspects of the mechanical response of the grains are highlighted, namely the scatter and the multiaxiality of the mesoscopic responses with respect to an uniaxial macroscopic response. Then, the distributions of relevant mechanical quantities classically used in fatigue criteria are analysed for some loading cases and the role of each source of anisotropy on the mechanical response is evaluated and compared to the isotropic elastic case. In particular, the significant influence of the elastic anisotropy on the mesoscopic mechanical response is highlighted. Finally, an analysis of three different fatigue criteria is conducted, using mechanical quantities computed at the grain scale. More precisely, the predictions provided by these criteria, for each constitutive model studied, are compared with the experimental trends observed in metallic materials for such loading conditions.

Study on Influence of the Load Path on Formability of Variable Cross-Section Y-Shaped Tube Hydroforming

Based on the analysis of now available evaluation indexes to estimate the formability of Variable cross-section Y-shaped tube hydroforming, an aggregative indicator is proposed. The effect of load path on the formability of Variable cross-section Y-shaped tube is discussed by FEM simulation, and validity of the evaluation index and simulations are proved by experiment. Results show that with the broken line load path of 0-30-30-40, the value of aggregative indicator is the greatest and the formability is the best. The optional parameters are testified by experiment and the results are in agreement with the FEM simulation results.

On the evolution and modelling of lattice strains during the cyclic loading of TWIP steel

The evolution of lattice strains in fully annealed Fe–24Mn–3Al–2Si–1Ni–0.06C twinning-induced plasticity (TWIP) steel is investigated via in situ neutron diffraction during cyclic (tension–compression) loading between strain limits of ±1%. The pronounced Bauschinger effect observed upon load reversal is accounted for by a combination of the intergranular residual stresses and the intragranular sources of back stress, such as dislocation pile-ups at the intersection of stacking faults. The recently modified elasto-plastic self-consistent (EPSC) model which empirically accounts for both intergranular and intragranular back stresses has been successfully used to simulate the macroscopic stress–strain response and the evolution of the lattice strains. The EPSC model captures the experimentally observed tension–compression asymmetry as it accounts for the directionality of twinning as well as Schmid factor considerations. For the strain limits used in this study, the EPSC model also predicts that the lower flow stress on reverse shear loading reported in earlier Bauschinger-type experiments on TWIP steel is a geometrical or loading path effect.

Yield surface of polycrystalline thin films as revealed by non-equibiaxial loadings at small deformation

A biaxial device developed at DiffAbs beamline of the SOLEIL synchrotron facility has been employed to determine the applied strains in film–substrate composites using both X-ray diffraction and digital image correlation measurements. Such an experimental combination is used for the first time to determine the yield surface of a polycrystalline thin film deposited on a polyimide substrate. In situ biaxial tensile tests under different biaxial planar load ratios were performed on W/Cu nanocomposite thin films deposited on flexible substrates. The effect of loading path on the yield stress of W/Cu nanocomposites is presented by considering a large range of proportional loadings. By comparing experimental results with theoretical models, this study reveals the brittle behaviour of W/Cu nanocomposite thin films at small deformations.

Crack path evaluation on HC and BCC microstructures under multiaxial cyclic loading

In this paper the multiaxial loading path effect on the fatigue crack initiation, fatigue life and fracture surface topology are evaluated for two different crystallographic microstructures (bcc and hc): high strength low-alloy 42CrMo4 steel and the extruded Mg alloy AZ31B-F, respectively.A series of multiaxial loading paths were carried out in load control, smooth specimens were used. Experimental fatigue life and fractographic results were analyzed to depict the mechanical behavior regarding the different microstructures.A theoretical analysis was performed with various critical plane models such as the Fatemi–Socie, SWT and Liu in order to correlate the theoretical estimations with the experimental data. A new approach based on maximum stress concentration factors is proposed to estimate the crack initiation plane, estimations from this new approach were compared with the measured ones with acceptable results. To implement this new approach a virtual micro-notch was considered using FEM. Moreover, the multiaxial loading path effect on stress concentration factors is also studied. The obtained results clearly show the effect of the applied load conditions on local microstructures response.

A different approach for considering the effect of non-proportional loading path on the forming limit diagram of AA5083

In this paper, the effects of strain path change on the forming limit diagram (FLD) of AA5083 sheet were investigated. The aim is to predict the forming limit curve (FLC) with non-proportional loading path by ductile fracture criteria. For this purpose, some square blanks were pre-strained by uniaxial tension in rolling direction (RD) and transverse direction (TD), and some others were pre-strained by biaxial stretching over a hemispherical punch. Then, the FLD test specimens were prepared by trimming the pre-strained blanks with the longitudinal axis in the RD and TD directions. The out-of-plane formability test was used for obtaining the FLD. The commercial finite element software ABAQUSE 6.9 was used for simulation in accordance with the experimental procedure. For trimming in the simulation environment, a program was written in MATLAB 7.6 that could determine the elements and introduce their properties to the new simulation model. Ductile fracture criteria were used for predicting the failure, and the Hill’79 criterion was used for applying the anisotropic coefficients. The results show that pre-straining in biaxial tension generally reduces the FLC and shifts it to the right-hand side of the FLD, whereas pre-straining in uniaxial tension raises the FLC and shifts it to the left-hand side. The numerical results were compared with the experimental findings, and relatively good agreement was achieved.

0104 F82H鋼における非比例多軸低サイクル疲労寿命に及ぼす負荷経路およびひずみ速度の影響(OS06-1 材料と環境,オーガナイズドセッション 6:「材料と環境」)

0104 F82H鋼における非比例多軸低サイクル疲労寿命に及ぼす負荷経路およびひずみ速度の影響(OS06-1 材料と環境,オーガナイズドセッション 6:「材料と環境」)

Multi-Axial Mechanical Behavior of Zircaloy-702 and Effect on Initial Texture

Zircaloy-702 (Zr-702 or UNS R60702) cylindrical tubes are commonly used for applications requiring mechanical stability in extreme environments. Owing to its crystal structure and processing techniques, significant texture and anisotropic mechanical properties are possible. In the current study, combined axial-torsional testing is employed to probe macroscopic stress–strain behavior in three dimensions, and corresponding yield surface in octahedral plane is obtained. Zr-702 tube samples are characterized under pure tension, torsion, and combined (tension and torsion) loading. Three-dimensional digital image correlation using VIC-3D system was implemented to determine surface deformation patterns for identification of strain localizations. Neutron diffraction-based texture analysis is performed to obtain an understanding of the effect of loading path on the material texture compared with the as-received, initial grain orientation. Pole figures for Zr-702 tubes are obtained for each loading path.